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Whiteboard showing the symbol for nullity (bottom)
The symbol for nullity (bottom)

1200-year-old problem 'easy'

Schoolchildren from Caversham have become the first to learn a brand new theory that dividing by zero is possible using a new number - 'nullity'. But the suggestion has left many mathematicians cold.

UPDATED: 13:45 GMT, 12 December 2006

You can now hear Dr Anderson answering some of the many comments and criticisms received on this page.

To listen to the full interview and read a transcript of a selection of Dr Anderson's answers, follow the link below:

Dr Anderson discusses NaN, peer review and binary, among other related topics.

Many thanks for your comments - the original article remains below.

Dr James Anderson, from the University of Reading's computer science department, says his new theorem solves an extremely important problem - the problem of nothing.

"Imagine you're landing on an aeroplane and the automatic pilot's working," he suggests. "If it divides by zero and the computer stops working - you're in big trouble. If your heart pacemaker divides by zero, you're dead."

Watch a video report from BBC South Today's Ben Moore, then let Dr Anderson talk you through his theory in simple steps on the whiteboard:
video Dividing by zero: Ben Moore reports >
video Dr Anderson's theory in detail >
Audio and Video links on this page require Realplayer
Dr James Anderson demonstrates his theory
Dr Anderson: 'it's that easy'

Computers simply cannot divide by zero. Try it on your calculator and you'll get an error message.

But Dr Anderson has come up with a theory that proposes a new number - 'nullity' - which sits outside the conventional number line (stretching from negative infinity, through zero, to positive infinity).

'Quite cool'

The theory of nullity is set to make all kinds of sums possible that, previously, scientists and computers couldn't work around.

"We've just solved a problem that hasn't been solved for twelve hundred years - and it's that easy," proclaims Dr Anderson having demonstrated his solution on a whiteboard at Highdown School, in Emmer Green.

Pupils at Highdown School
Highdown pupils: 'confusing at first'

"It was confusing at first, but I think I've got it. Just about," said one pupil.

"We're the first schoolkids to be able to do it - that's quite cool," added another.

Despite being a problem tackled by the famous mathematicians Newton and Pythagoras without success, it seems the Year 10 children at Highdown now know their nullity.

last updated: 12/12/06
Have Your Say
Do you understand Dr Anderson's theory? Has he shown enough workings to earn full marks with you? Could your maths knowledge be divided by zero?
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The BBC reserves the right to edit comments submitted.

The first problem I see with this idea is that the definitions are not well defined. Consider 1/0=inf. Then inf=(1/0)*(-1/-1)=(1*-1)/(0*-1)=-1/0=-inf.A similar string of equalities gives 'nullity' being equal to both inf and -inf.

"Imagine you're landing on an aeroplane"Landing ON an aeroplane? which part of the aeroplane should I land on?

I like how he never really proves anything. All he says is "0/0=nullity." Okay? What's wrong with saying NAN? "Well," he would say, "Nulity is actually a number." Well that's great, but why cant you add it,subtract it, multiply it, divide it, do exponents, or do roots with it? Why does it mess of everything we already know about math? If the only difference between this "nullity" and NaN is that "nullity" is cnsidered a number, then I have an idea. Why not say "aN" for "A Number."

x divided by x is always 1, so why would 0 over 0 be any different, it should be 1

First of all, if you are so opposed with the definition of a number nullity=0/0, why do most have no problem with the definition i^2=-1?? there is no difference in the fact that they are both definitions of a non-real numberMost of the comments here also keep using the 1=2 fallacy. This fallacy uses the assumption that 0/0=1, which is not true in transreal arithmetic. In transreal arithmetic, you would get the result nullity*1=nullity*2, which is true.Also, the limiting process is not important here, because it only looks at values close to the number in question, we could define the actual number as nullity without losing the concept of limits.Nullity is different from NaN, for the simple reason that, while NaN does not compare to itself, nullity is equal to itself. Every time.Even if we have no use for it now, who says we will never discover one???

How do we solve an unsolvable math problem? Make a new number and say it's the answer!!!

Very nice site!

"nullity - which sits outside the conventional number line (stretching from negative infinity, through zero, to positive infinity)"Nothing over Nothing = Everything? This doesn't make any sense to me...

what he is saying doesn't make sense. it's better to say that x/0 is infinity, since any number would fit in it. Assuming 0/0 is that nullity thing, does 0 times nullity equal 0? explain that on his number line. How come when you graph x/0, and you look at the 0 point, the line is really at infinity? He obviously thought that he could just do what people did with square rooting negative numbers, which he can't, since the square root of negative one actually does exist, just not in the real number system. dividing something by zero isn't impossible, you just can't do it. Imagine you have a trillion apples. You want to divide them evenly between zero people. How many does each person get? theres no people to give the apples too. It's not like every person gets nullity, there's just no one to give anything to.

Rajiv Amlani
Teaching kids a pile of rubbish. Shouldn't be teaching mathematics if you think 'nullity' solves a 1200 year problem. Clown.

He claims that 0/0 is nullity, a single number with a definite (albeit not strictly real) value, yet we know every real and complex number solves 0/0=x, so it is not a single number, it is undefined, it really is that simple. What he is saying is simply incorrect. Also 1/x as x tends to 0 does tend to infinity, but 1/0 (and indeed a/0 where a is not equal to 0) is not equal to infinity, it is indeterminate, which is to say there is no value which solves 1/0=x. Infinity is not a number it is the concept "as large as we want", for 1/0 "as large as we want" is still not large enough.


it's basically the concept of imaginary numbers, except those are actually useful sometimes.

very clever one
Hey! i just found a way, how can EVERYONE multiply two numbers just in a sec or two! Let's say, that every number which is greater than multiplied by ANY number is equals to BIGGETY. I hope i helped all the mathematic and big number problems, maybe solved the spaceship problems as well.

Kenneth Wong
This would defeat calculus. On a limit, the undefined is usually really important. To my understanding. Im still in middle school.

I. Hate. Him. That guy is a cheat. He just says 'Oh, hey, this here is a new symbol I "made" whose sole purpose is to divide by zero!' A lot of good that does us.

the "we use 0/0 in calculus" argument is stupid. people, we do not get the value of 0/0 in calculus. we get its limit. there's a difference.

Bernard Azakie
British schoolchildren "stupid"Have a nullity doesn't change anything. Your system will spit out "nullity" upon crash, but won't actually change anything. Whether something crashes gently or not is just a matter of crash handling.

EXPANDING FAILLLL YUSHIN WASHIO.x*(y/x) = y if x and y are INTERGERS not equal.If you expand using zero, it will clearly give zero.Division by zero is NOT POSSIBLE using the RNS. nor is finding the SQRT of -1.

Sam O'Nouny
"Nullity" is utter bupkis. It's just another way of saying "Not a Number", "Undefined", "Indeterminate", and of course, "Error". One cannot divide or be divided by zero. After all: 0/0=X; 0=X*0; therefore, X=All Real Numbers, causing it to be undefined. Or is it +inf and -inf? *shrugs*PS-Rearrange "Sam O'Nouny" and you get "Anonymous".

Yushin Washio
Similar to the imaginary unit, it would be more useful to define 1/0 rather than 0/0 becuase anything is 0 if you multiply it with 0. So, 0*1=0, 0*0=0, 256*0=0 and even i*0=0. So, 0*(1/0)=0. However, since always x*(y/x)=y, 0*(2/0) must be =2, 0*(3/0)=3 and 0*(i/0)=i should all be right. Therefore, if 0^-1 is not simple enough for you, you can define your "nullity" as:0*1*nullity=1but 0*nullity=0and 0*-1*nullity=-1However, since the nullity itself without 0 is not defined, 1*nullity or -1*nullity remain undefined.
great news, now tell me how can i get my ten year old to learn divisions .. he knows his time table in head from 1/15 times but he just cannot understand divisions no matter how hard i try please...

Siyang Chen
This is neither new nor useful. Computers already have the equivalent of a 'nullity' (NaN) in every reasonable floating point data type. Moreover, this does not reveal anything about dividing by zero that we did not already know (meaning, that the operation cannot produce any meaningful result with other arithmetic operations). Hooray for relabling an old concept and claiming credit for it. Maybe I'll go discover gravity tomorrow.

This is bullshit and he SHOULD know better. If he'd asked any one in the mathematics community he'd have known he wasn't solving a problem because there was no problem to begin with!He hasn't even checked to see all the contradiction his theory presents.There are tons of ways to work around the problem, the projective line being a very practical example. AND they those ways are more theoretically sound and non-contradictory. I won't bother to explain it because obviously no one is interested in hearing real mathematicians talk. It's not like we just spent our last five years intensely studying it or anything. Never mind us.

Take the blue pill, Mr Anderson.

1*0=2*0divide both by zero (which is an immposability)and you have 1=2this number CAN'T be realand even if it was zero is the concept of nothing...infinity would be everything and so cancel it out not "nullity"

This is ridiculous. Dividing by zero is not a "problem," it's a mathematical impossibility. Inventing a name for an entity that doesn't exist doesn't cause that entity to exist.Look at it this way. You tell me there's no animal made out of cheese. I say yes there is, it's called a froopsie. And then I write, like, twelve papers based on the existence of the froopsie and how I've solved the cheese-animal problem. The froopsie still doesn't exist, and I haven't solved the problem.Not only is Dr Anderson displaying a basic lack of understanding concerning why this "problem" can't be solved, but he's passing it on to those poor schoolchildren. Maths education is bad enough already. This man should be stripped of his teaching licence.

This whole idea is utterly pointless. This man is just making up a new word for NaN, or undifined. And if someone can come up with a practical use for this, I won't belive it.

This new number has profound effects on the computing industry, by allowing the division of zero by zero many errors that have previously made things impossible have become quite possible.

Aaron J. Lang (
I'm currently studying maths at GCSE but am one of if not the top in my year. The equations he does on the right are hard to read in the video but I have a problem with the "definitions" he puts up on left, he simply states them, no explanation or deriving or anything. If anybody knows where I can find this then please tell be, if not then his theory is just too unsupported to be taken seriously. P.S. I sure the greek letter "phi" that hes using for "nullity" is already assigned to (((5^0.5)+1)/2). if its not and im being really blonde please contact me (address above), i really would like to understand this.

Tayler Wampler
OK well I think this guy is quack. If you *can* divide by zero, then wouldn't everything in Math be a lie? And pretty much, this is so useless. Who's ever gonnahave to divide by zero? People have been doing Math how we're doing it now for.....I hesitate to say forever.....but a *very* long time. What's this guy trying to do, anyway? Create a revolution? Not gonna happen.

i thought zero plus zero = zero. i also thought zero divided by zero was zero???

x * 0 = 4 Solve for x.

I always knew that such a number existed, if you take out your Ti-83 plus, on the graphic section, you write 1/x, you can see in the graphic that a nomber that would represent 1/0 would be all the number, wicht is imposible in a fonction...

Its not such a big deal. I mean c'mon so there is a new number that noone is going to use anyway. Woop-de-de,How many times are you going to divide something in real life by 0 anyway. It is just one of those pointless questions they stick on an exam.

I todally do not get it. I mean how in the world can 0/0=infinity? It is just plain cofusing! I guese that it might make more sense when ever I get taught it, but untill then I guese that I will just have to be confused. Ta, Ta for now!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

This is stupid. It 'solves' nothing. It still, basically, says that X/0=NaN. It's a useless concept. Perhaps it will help computors, but it changes nothing mathimatically.

that guy
i just divided my pacemaker by 0, but i havent died yet

a high school physics student
another thing... phi is already a symbol for flux... nothing new

a high school calculus student
calculus - where we divide, add, subtract, and multiply by zero and infinity go get real answers all the time...

nikko holt
i think this guy needs to go back to the drawing board. i don't see why they let him teach this to kids like you always say make complicated things simple he's making things way more complicated.

ron jones
one divided is technically ifinity

Fantastic! Extra stuff to learn at school!

This guy basically put some sounds together, drew some lines and got a word and a sign for undefined. yoopdeedoo. The amazing part is he confused one of the first things i learned in elementry math, you cant divide be zero. This just messes up the way i think. It goes against 'the essence of mathmatics is to make complicated things simple. Not make simple things complicated.' It just doesn't work Mr.Frazier.

Alexis Peneff
Kind off It would confuse me at first. But after a while i would get it. The theory is a bit strange. It will take even more years to get the calculators and computers to have nullity. I dont think that my math knowledge couldn't be divided by zero. It would take my brain a lot longer to get this know then if someone created it when i first started math. My brain is already used to the old fashion way. Other wise i think it is a good theory. Though i have never tried to divide by zero.

Sameera. K
I am doing a physics coursework in which i am investiagtign whether how the thickness of the wire affects the resistance. However on one of my graphs, which is one over thickness, my teache rhas asked me whether or not the graph has to go through the origin. But I found out that one over zero equals infinity, thereofore how can that be represented on a graph? However if thinking logically is there is zero thickness then there will have to be zero resistance. This is why I ma quite confused.

0/0 = X 0 = X * 0 So zero times what equals zero. Thats right boys and girls. Every single number that exists. ... This is why it comes up undefined. DUH... If they want to come up with a symbol that represents any number, go for it. But its kinda pointless. 0/0 = anynumber, it equals 1, and 2, and 50 and 100 and 5000, and 2^58, and 281! and sqrt(1.52x10^235409) and 0 and i and -i... etc etc... Do you get it yet? No DEFINATE answer. the answer is a variable that covers all possibilities.

What the hell? Making up another number is not solving things -_-

a great number of the below comments point out the various flaws in dr. anderson's idea. the value in it (if any) is that in mathematics you can define any element you want, as long as you are consistent with the accepted axioms and conventions. from a mathematical standpoint dr. anderson is just being silly, from an educational standpoint he's teaching his students a bit about how the mathematics progresses and how it has become the field it is today. unfortunately, he’s not consistent with that which has come before him.

many people are forgetting, or simply haven't worked with higher math, but in calculus classes they very often work with problems that would cause division by zero. In many of the problems its as simple as changing some of the variable to more integratable or differentiable variables and derivating or integrating... take a calculus class before relating conjecture that you know, obviously, very little about. Oh, and P.S. the solutions to many of these problems varies with each circumstance and the equations chosen, so, e.q. 0/0 could equal 1 or infinity or a set number.

The Anonymous Rho
I think everyone is delving too deep in the operation of division. Division, in its simplest form, is repeated subtraction (by its very definition). So, 20/5 is 4 because we can subtract 5 four times from 20 until we hit zero. So, let us examine 1/2. This equals one-half because we can subtract 2 one-half times and get zero. Great. Now, 0/1 is zero because we need to subtract 1 zero times from zero to obtain zero. Fabulous. What about 1/0? How many times must we subtract zero from 1 to obtain zero? Oops! That can't happen. That's why 1/0 is undefined. What about 0/0? How many times can we subtract zero from zero to obtain zero? Well, this seems indefinite. Could be 1, 2, or 1x10^2001. So, 0^0 is also undefined. Dr. Anderson makes conventions for the sake of making conventions; we can define 4/2=infinity. That's a convention. Let's not mention the fact that Dr. Andersen uses the laws of exponents for his lousy argument or that the laws of exponents only work for real numbers, so his arithmetic does not work with his new number 'nullity'.

Okay, so he basically gave x/0 a new name, and completely against the meaning of 0/0 (see l'Hospital's Rule). I fail to see how this is revolutionary, unless re-naming stuff and making it convoluted is revolutionary. If that's revolutionary, I'd like to announce a revolutionary concept of my own: Plard. It's a constant that's between 0.5 and 0.6, approximately 0.573. Now gimme a Nobel Prize for my revolutionary concept. Also, the computer science aspect already has a perfectly good solution - the try-catch statement.

So essentially he just took the word "undefined" and gave it a symbol that he's calling nullity? I'm sure there's more to it than that, but that's what it looks like to me. Just trying to give computers a way to understand "undefined."

I think Dr. Anderson just proved the existance of god....

I know the exact type of person this guy is; we all do. He's that guy who is always trying too hard to be positive, to listen to everyone's ideas, and to think, to actually BELIEVE they are correct. My deputy principal is just like this guy. I can see this guy sitting in his office, or wherever, talking to his buddies saying "i don't see why everyone thinks this whole 'divide by zero' thing is so hard. Why not just create a new number to account for it? It's really quite simple". Thinking about the theory itself, like someone mentioned previously, dividing 6 apples by 2 give 2 groups. Thus dividing by 0 gives 0 groups. Also, when multiplying the previously exampled two groups by two, you get the original six. If you have divided something into nothing, then multiplying backwards by any amount, will still give nothing. Thus proving anything(besides 0)/0=0.

Look, here's how it is. x^1=x, right? And to get x^0, you divide x^1 by x. We already know that x^1=x, so we can say that x/x=x^0. This is the obvious part. Now, if we make x = 0, then we're saying that 0/0=0^0, or written differently 0^0=0/0. Dr Anderson is saying that 0^0=nullity. He already said that nullity is just 0/0. So basically he just proved that 0/0=0/0. Which is great.

Joe Whitehead
I was sure that was not the only one to think of 'innumeracy' constants! It's cool to see someone finally find a use for them. The problem is that the division isn't reversible. ;) The fact that one infinity may not be the same as another is another issue all together.

Math fan
To Kevin: It is not 1 divided zero times. It is 1 divided into 0 groups. When you have 1 divided by 2, you are not dividing 1 two times. That would create 3 groups. You are making 2 groups. So the problem arises when you try to make 0 groups. Also, there is the principle that 0 divided by anything is 0. In the case of 0/0, it contradicts the principle that anything divided by itself equals 1.

this is just ridiculous! there's no consistent way of defining a division by zero as a number. you will only end up in inconsistency.

NO! you can't divide by zero. it's impossible. i will cry if you can divide by zero. no lie. it will prove that every single thing in math was a lie. i hate math.

Okinaptz Uglwf
So "nullity" is "outside the conventional nubmer line". In other words, nullity, as x/0, is not defined "inside the conventional number line". Big deal, really ...

Some guy
Division by 0 is not possible. Just look at the graph of 1/x. As x approaches 0, f(x) approaches +/- infinity. For this reason, anything divided by 0 cannot be 0, as somebody else said. Plus... If x/0 is defined, then you can prove that 1=2.

Having encountered Dr Anderson at university, I have a more specific comment. He could do with marking some students work instead of spending his time naming undefined numbers. Here's my new number - it's called 'the answer'. Give me any problem - the solution is my new number. In conclusion, Dr Anderson is a computer scientist and not a mathematician - there is a world of difference.

the problem i have with this, is its not really math, they are inventing a number to fill in a missing piece of a puzzle, which is *far* from complex math. dividing by zero does not give anyone any ANY useful mathematical numbers OR formulas, it is the same if the result is "nullity", which would really be no different then an error message: it still serves no purpose to mathematics as a whole. spending your life calculating pi and trying to find an end is more useful then "nullity" (mainly because it would keep Dr James Anderson busy so we wouldn't have to endure more of this kindergarten math... summary: if you could just invent a number to solve a thousand year old math problem A. its takes away all legitimacy of said problem B. Roman mathamaticians could have easily thought of it: if it was a good idea (which it isnt)

What about this? 0 = 1 / ∞ 0 = 0/1 0/1 = 1/∞ (Cross multiply) 0*∞ = 1*1 The sum of infinite 0’s still amounts to 0 so: 0 = 1. Isn't this the same line of thinking?

For those interested in understanding the topic of zero, I recommend Charles Seife's book, "Zero: The Biography of a Dangerous Idea." Of particular interest is the first appendix, which uses the 0=1 proof to show that Winston Churchill is a carrot.

2 divided zero times is not two. Dividing it zero times gives you zero parts of a sum. Imagine dividinig 2 a half a time if you can. You get 4. Dividing two a quarter of a time gives you 8. Take this infinitely close to zero and your answer approaches infinity, not 2.

Senor BS
This is utter BS. 0/0 is the exact opposite of "Nullity". It's defined as some number which, when multiplied by zero, would equal to zero. This means that 0/0 is equal to ALL numbers, rather than none. BS.

I think part of the problem arises due to the way zero (0) is used alternately to represent void (nothing) or the infinitely small 1/inf. Void isn't 1/inf, void (0) would be more appropriately linked to "Not a Number" (NAN). The infinitely small still has size and infinite progressions never reach zero. It's always puzzled me how slack mathematicians are when considering stuff like this. Far from being rare probs like this crop up all the time in computing and programmers can't use sloppy maths to work around it. 1/0 would therefore be better represented as 1/(1/inf)=inf perhaps we could have a new symbols such as Q to reprsent the infinitely small and use 0 to represent nothing or "no number". Thus div by zero would be x/q=inf

I think part of the problem arises due to the way zero (0) is used alternately to represent void (nothing) or the infinitely small 1/inf. Void isn't 1/inf, void (0) would be more appropriately linked to "Not a Number" (NAN). The infinitely small still has size and infinite progressions never reach zero. It's always puzzled me how slack mathematicians are when considering stuff like this. Far from being rare probs like this crop up all the time in computing and programmers can't use sloppy maths to work around it. 1/0 would therefore be better represented as 1/(1/inf)=inf perhaps we could have a new symbols such as Q to reprsent the infinitely small and use 0 to represent nothing or "no number". Thus div by zero would be x/q=inf

Question. What's so difficult about the thought that 0 divided 0 times is still 0? 1 divided zero times is 1? 2 divided zero times is 2? This is division right? That or if it's fractional the answer is always 0. Is that where this whole bit comes in? -Kevin

i learned that myself when i was 8 thanks!

Bah. This is ridiculous. Why not just say that 1/0 equals infinity and proceed from there? You know, like mathematicians do ALL THE TIME? The only problem that leaves is 0/0, and you only get that in places like weird limits, in which case math has more than enough fancy tricks to go around (like LaPlace's theorem). And that nullity symbol is just a capital phi. Not very inventive. Also, I would like to state for the record that anybody who can say "Imagine you're landing ON an aeroplane..." with a straight face should not be teaching anybody any sort of high-level math. Not to mention the fact that even Bush isn't stupid enough to consider the possibilty of a pacemaker dividing by zero.

The CS field already has a designated way of referring to what you get from dividing by zero - floating point has a defined NaN - NOT A NUMBER. You cant perform any arithmetic on Not a Number. If you COULD perform arithmetic on it, it would be trivial to "prove" that all numbers are equal to all other numbers - its a common mathematical brainteaser to give a series of expressions that ends with " 1 = 0 ", with one of the steps being cleverly disguised division by 0. Think of it, you have six apples, and you need to divide by two - you divide the apples into two groups (of three) Even on this simple explanation, if you were to divide by zero, you'd need to divide the apples into zero groups. It doesnt mean anything.

Professor B. and Hmmm your both right. It is the lamest theory and in programming we do have that exception handling to deal with problems that may cause things to crash... I think this guy just want to get into the news and be seen... So he will invent any solution to problem or theory that would give five minutes of fame. As for teaching school children with lame theory as this nullity is stupid.

it just sounds like there giving something a name rather than just saying it's an unknown factor...

The biggest evidence that this has no mathematical basis is that 0/0 is different from any other real number divided by 0. 0/0 is not undefined. It is indeterminate. As an undergraduate math student, I have solved 0/0 in several problems. Sometimes it's undefined, sometimes it's 3, sometimes it's e, sometimes it's can be anything. If I can understand this as an undergraduate student, I worry about how he received his doctorate.

Wow...slow news day huh. This is absolutely absurd. This is similar to that silly 2=1 proof that gets whored around the net. Zeros cannot simply be cancelled out.

I think this idea is very interesting. Why? Because we need ideas to redefine the basics of our knowledge to solve and cover more problems. Our goal is to solve more problems. When this idea helped to solve some unsolved problems, then you may think that this idea may be the single bright idea of the century or even the millenium?! However, it is to soon to judge that :)

Poly Ester
So you found a symbol for undefined. You're soooo clever!

This is just pointless. Dr. Andersen is just making a dumb "new number" that will change many things for the worse. It will make programs harder to write because we now have to know when nullilty will be used. Its a nice idea, but not thought though enough. Anyways, the onlypeople who will understand this without complaining are students who havent heard about this topic yet. For everyone else, it will confuse you even more. i think that this is the dumbest thing that ever happened to the world of mathematics. Its like changing the word mathematics to hahehahe. It confuses and makes no point. One more thing, what is that part about "nullity", being in a new number line, that must have been a little kids's thought.

Nicolas Capens
I've read parts of Dr. Anderson's articles now, and my biggest gripe is that he doesn't really solve anything. Certainly not division by zero. He redefines 'undefined' to prove that the undefined of 0^0 is the same as the undefined of 0/0. I believe this is correct (at least in his algebra), but it doesn't really help us. Airplanes will still crash when dividing by zero without handling the exception. I propose a number Q^-1 that is defined as the number you have to multiply 0 with to get 1 (just like the imaginary i is the number you have to multiply by itself to get -1). Just like i solves the problem of working with the square root of negative numbers, in practical situations, Q^-1 solves the problem of working with the division by 0. Also, i is physically meaningless unless you multiply it with i to give -1, and Q^-1 is meaningless unless it's multiplied by 0 (which is equal to Q, Q^-1's reciproke) to give 1. The most important axioms: a = a*Q^0. a*Q^z / b*Q^w = (a/b)*Q^(z-w) {b !=0}, a*Q^(z-w-1) {b=0}. a*Q^z * b*Q^w = (a*b)*Q^(z*w). a*Q^z + b*Q^z = (a+b)*Q^z. Applying it to 0 / 0 gives 0*Q^-1. So that multiplication by 0 gives 0. Because Q is orthogonal to i we can actually define a three-dimensional space. For example the square root of -1/0 would be (0+1*i)*Q^-0.5. 0^0 does not seem to be 0*Q^-1 though...

Edward Cherlin
NaN has been a feature of IEEE floating point arithmetic for 20 years. Before that, the non-values Bottom and Nil were used in Computer Science for all functions that didn't have proper values. The real number line and complex plane have been extended for well over a century with an infinite value which makes them topologically complete, and Conway numbers can handle arithmetic on infinitesimals of all orders. Alternatively a plane can be extended with a line at infinity, as in projective geometry, and all of the points at infinity can be represented in homogeneous coordinates using only finite numbers--the sort of thing your graphics card has to do to manage the apparent meeting point of parallel lines. Painters learned to make lines at infinity work back in the Renaissance. You can look all of this stuff up on Wikipedia. So this is trivial and not news at all to artists, hackers, or mathematicians.

Rick Burgin
I would've discovered this a long time ago if I'd have realised I could create my own number outside the "conventional number line". It's like playing a game and making your own rules up as you go along. What a failure.

Whay cant we focus on curing cancer instead of making up numbers? Seems to me to be a better use of our time.

Nicolas Capens
Correction to my previous post: Numbers can't be both a division of zero and a multiple of zero at the same time, so only one bit field suffices. I also have a better notation: Lets write 5(/0) as 5*Q^-1 and 3(*0) as 3*Q^1. And define Q^0 as 1. So it's an algebraic object like the imaginary i. So in our binary representation we only have to store the exponent of Q. Real numbers have a Q exponent 0. Divisions by zero have an negative Q exponent. Multiples of zero have a positive Q exponent. With just two bits we could prevent up to double division by zero exceptions. © 2006 Nicolas Capens

I believe there is one use for the term of nullity. Nullity equals Dr. Anderson's IQ divided by the product of Dr. Anderson's supporters. That being said, I agree with the comments made by the majority of the responders. Nullity is merely a new word to say that it is either undefined or defined as itself.

Nicolas Capens
This approach has only (limited) use in computer science. Say we need to compute a * b, but an external library only gives us a / x. So we have to multiply with b * x, but if x = 0 then we get NaN and not a * b. The solution is to keep the numerator when dividing by zero, and set a bit that indicates division by zero. Say a = 5 then we could write 5 / 0 = 5(/0). Also when multiplying by zero we keep the original value but set a bit that indicated multiplicatio by zero. Say b = 3 then we could write 3 * 0 = 3(*0). When multiplying a and b we get 5(/0) * 3(*0) = 15. The (/0) and (*0) bits cancel each other. So basically 0 / 0 is still undefined, but (a / x) * (b * x) is defined as a * b. Obviously, this doesn't really solve anything, because the software should be able to compute a * b directly. A well designed external library has to provide a separately as well. It can effectively avoid division by zero crahes in badly written software though. But it still has its practical limits. If we have (a / x / y) * (b * x * y) then we need extra bits to indicate double division by zero and double multiplication by zero (four bits actually suffice for up to triple division and multiplication by zero). Even if we add those there would still be an exception and a potential crash when dividing by zero four times... © 2006 Nicolas Capens :-)

i think that this is pointless

Professor B.
This has to be the single most lamest theory so far this millennium.

""Imagine you're landing on an aeroplane and the automatic pilot's working," he suggests. "If it divides by zero and the computer stops working - you're in big trouble. If your heart pacemaker divides by zero, you're dead."" It's called exception handling...

Well, complex numbers were not considered before but now we see its application in the real world. So, let's find out if the theory about nullity can pass the mathematical community. Thus, how will we call this new set of numbers (with nullity)?

Arnold Schmidt
To see the failure of Western citizens to achieve any degree of basic mathematical literacy, look no further than this idiotic piece of "journalism." "Dr." Anderson's "nullity" symbol is neither theory nor discovery; it is merely a publicity stunt by a hapless "professor" who realized that BBC reporters are, to put it mildly, dumb. This article is an embarassment to the mathematical community everywhere.

it sounds like he's suggesting that dividing by zero leaves you with a value that represents the set of all numbers from -inf to +inf... IE: infinity. We already knew that dividing by zero left us (basically) with infinity. This is fairly stupid.

The Wise Man
An infinitely null idea amounting to nothing.

It seems that people are very content to name something, thinking it will help. But it's just a convenient tool that doesn't go anywhere. Until I see where it is useful, where this new symbol holds any more meaning than 0/0, then I'm not convinced.

roy bob
I heard that miscrosoft is running a new service pack to update their OS. - if we knew this theory a year before most of our security updates would make nosense. This is the desmonstration that we where right, our software is the best, but we couldn't manage what we don't know. All our programmers are older than 16, so they know nothing about nullity. Intell is now working with apple to solve the problem in future versions of their processor. - We are really scared about implications: we are still evaluating how far do we have to go developing a new ALU for this. So we'll know much more in the future.

This is me, I got solved. btw, the problem is not this theory, solving an inexistent problem.. We allow a stupid operation, divide 'nothing' into 'something'. I remember I was told to do NOT add 'pears' and 'apples' because "it can't be done". Lets go further, avoid any mathematical theory regarding "0 divided by", just because it can't be done. For now lets name this brand new theory the "End Point theory". Whenever you find the "0 divided by" patter, stop, as it can't be done. mm better if go one step further, Lets doubt the axioms of the actual theory: Instead of trying to solve the solution 0/x, consider the problem this kind of situations, "if this way leads you to 0/x, then your way is wrong from the beginning", don't turn the solution a new problem. I'm the only one who thinks that maths where created and can also be changed? or we still must to thank god for this?

Dr Charles Allerston
The length of this thread clearly proves that infinity exists.

I think 0/0=nullity="Nonsense!"

Uncle Dave
I love this. Using nullity I can now complete my design for a perpetual motion machine. Patent Office here I come!

Nullity solves nothing. It's a new way to do the same thing- that is, nothing. Nullity still can't be manipulated into any form of use other than the uses other concepts have fulfilled via calculus equations. He's just trying to make it seem like he invented something, when he just reworded it in essence. And shame on the BBC. I always thought they were smarter than to actually publish something like this.

seymore buts
well if you had 2 apples and put them into 0 groups then there wouldnt be any apples because there is no group to put them into right? that simple...

Tomek Perlak
Re: a physics proof --- But haven't you just proven that the first equation does not 'always' apply, hence a better one, including both the mass and the frequency should be applied? --- Please, note, this is said from a 'mere mortal' point of view --- and yet, what you've said could point to a conclusion that mass and frequency are not really two different concepts, but more so two different 'interfaces' to the energy in matter? --- Anyways, if there are two equation in use for energy, I would also 'allow' for two different cases with 'nullity' in them; just a thought;

Jason Dick
The stupid thing about this is that mathematicians have been dividing by zero for quite some time. It's basically a requirement to do any calculus. The concept of nullity adds exactly nothing whatsoever to mathematics: we already have well-defined concepts for how to deal with division by zero. This is, essentially, the same as somebody declaring that he or she knows how to take the square root of -2, calling it negativity or some such.

Interesting, but...
Nothing from Nothing Leaves Nothing! Billy Preston 1974

This is the most pointless BBC article since "Sudan Man ordered to Marry Goat". I feel terribly sorry for any of his pupils, that upon taking maths above GCSE will find that their genius of a teacher has in fact taught them total rubbish. And of course the fact that Transreal Computing Ltd requires publicity has nothing to do with this ridiculous claim.

Nikolas Bourbaki
I find the results very interesting, after having read the explanation on Wikipedia. Please read further before going too crazy, he is working with "transreals", not the Real number system. Perhaps it would be better if he also invented a new symbol for his trasreal zero, unless his zero is real, I'm not sure what the case is. Oh well, I think I'll go sharpen some pencils demurely and give my sliderule a wipedown before retiring to the library.

Perhaps this is a good time for me to discuss my own recently published research. 1.9999... repeating is "pseudo2". In every respect it is like the number 2 except that the result of arithmetic operations using pseudo2 are decremented by 1 and added to 0.9999... repeating. This brings me to my next research topic called "pseudo1" which I am currently working on, but all I will say for now is that it requires a radically different take on how we see mathematics and could have revolutionary benefits for computing. If you don't believe me I'd be happy to show you working protoype applications demonstrating my research.

Christopher Joyce
I'm confused? transreal arithmetic states that ln[-1]={PHI} where as complex arithmetic states that ln[-1]=i{PI}; so while transreal arithmetic considers ln[-1] to be nullity (and not complex), complex arithmetic considers ln[-1] to be complex (and not nullity), so aren't transreal and complex arithmetic inconsistent?

Joe Barkun
I didn't really understand the real use for this "new" theory... And could you please use it in a LOGICAL MATHMATICAL equation or application...

"sits outside the conventional number line"... in other words, it isn't a number? That's cute.

i don't see what the great point is though, it needs purpose. dividing nothing into no equal groups (aka 0/0) i don't think will do us any good. with the lack of value divided by the lack of value your not getting anything substantial and to any power except maybe the zeroeth power it remains the same. If there will be a use for it i really hope i get to see it. And no uses are stated although it says it has use. "Make all kinds of sums possible"

you do realize that if this is true then 2 now equals 1. see this proof: assume a=b so starting: 1.a=b 2.aa=ab 3.aa-bb=ab-bb 4.(a-b)(a+b)=b(a-b) 5.a+b=b 6.2b=b 7.2=1 the only thing keeping this from being true is step 4 to step 5... division by (a-b). since a=b then a-b=0, and division by zero making the proof false. he just made 1=2... yeah have fun with math now... when 1+1={1,1.5,2,3,4}

Nullity seems no better to me than undefined... what's it equal to? How do you use it in sums? Where does it fit on the number line? Does it need a different axis, like i? I need a good definition, then I'll think about it.

Karl Babbitt
Why not accept that YOU CAN'T DEVIDE BY 0!? Nullity is a very bad idea, looks like a caveman came up with the symbol.

Rainer Raisch, Munich, Germany
multiplying with zero always gives the result zero. Its not reversible like infinity as result of the division x/0. This "problem" needs no cure.

It's clear that this had to come from a computer "scientist". Any secone-year math student would take it apart within seconds. I just wonder how BBC fell for that nonsense, I thought higher of them.

To be a good theory, a scientific theory must among others be relevant to real-world problem solving. Other from that, I must say it's an honor to have Mr. Norris comment on this page. Thank you.

Axioms 19 and 20 are troubling (bijectivity of reciprocal and 1/0 = infinity). Doesn't sit well with calculus.

Arturo Martinez
Dr. Anderson: Axiom 16 (NULL=Inf*0) is not at axiom at all, check: NULL=-NULL -> A9 1*(0/0)=-NULL -> Definition of Nullity 0*(1/0)=-NULL -> A13 0*INF=-NULL -> Definition of Infinity in R^t 0*INF=NULL -> A9 I'm still not sure if R^t can build a consistent algebra

Richard R.
This is perhaps the stupidest thing I've ever heard. I am led to believe that neither Anderson nor the journalist of this article possess a mathematics proficiency higher than these students who are being lied to.

Braindead Dan
Well, shouldn't 0^0 = 1? Because 0 divides into itself once, like any number divided by itself 1^1 = 1, 2^2 = 1, etc... Just my thoughts.

Jorian Hoover
I think I've got it. This "nullity" is prety much the same as undefined, but easier to express on paper. I wonder how fast this will spread around. -Jorian Hoover

Zach M.
Being a senior in high school, I see this and think, "Well, I won't have to worry about this." Then I realize I'm about to head into college. Well, now that I've heard of the concept, at least I can mentally prepare myself for it. And if this keeps up, I'll just have to keep myself mentally prepared when we run out of letter variables and start using animals.

Bob Binkman
I find it quite interesting how Pythagoras got to work on a 1200-year old problem more than 2000 years ago. :)

Vader Piet
If you guys like real math about infinity, please read the book: "The Mystery of the Aleph: Mathematics, the Kabbalah, and the Human Mind" or just search for Georg Cantor and why he spent his last hours in a mental institute.

*LOL* I think people should be less angry at Mr Andersen and direct their ridicule at BBC for running such a hilarious article. Bravo BBC, you're competing with the tabloids for the quality of reporting. Any beginning calculus student knows that the concept of a limit resolved the division by zero problem ages ago. The fact that computer returns an error does not mean there is a problem - it simply means that it is incompetent to use the computer output without thinking about the round-off issues and the like. Millions of professionals use existing algebra to calculate anything from portfolio allocations to space shuttle trajectories, and I can assure you that any future Mars expedition won't miss its orbit for the want of nullity in its computer system.

Caoltan Strain
stupid. doesn't prove anything/ make anything any better. its still, in reality, undefined

Jimmy Johns
According to Jake`s theorem, when Nullity is plugged into the quadratic formula, we find that Nullity is obviously equal to (1-C). Therefore, (1-c)^2-(1-c)+C = 0; And in effect C=0. Thus proving that nullity equals (1-c), or 1.

Sara Postma
You are my hero!!! i love you!!!!!!

This might be useful for pedagogical purposes, since it's often uncomfortable for students to learn that some things simply "don't exist" (like 1/0), but it has very little scientific value. Computer programs still can't divide by zero, but they work around that by handling those sorts of exceptions. This is just another way of handling the exception, so to speak. From a pure math standpoint, I'm afraid it's completely useless since the addition of nullity to the reals would keep it from being a field, or even a ring (0/0 * 0/1 = 0/0, but a*0 =0 for all a in a ring), so multiplication would fail. And without multiplication, there's no need for 0/0 because it requires the concept of division. From a topological standpoint, it's already been done, since 1/0 is treated as infinity in many ways when constructing complex conformal maps, for example. It's also a bit crude to pretend that this has even been a problem, that it has been a problem for 1200 years, and that some guy just came along and solved it with the mathematical equivalent of rewording the problem. It seems the best quantitative description of the worth of this supposed discovery is nullity itself.

Gregory C.
Maybe Dr. Anderson's brain tried to divide by zero.

David N
I suppose everything would be just fine if your pacemaker tells you that your next hearbeat should be in nullity milliseconds instead. This theory is neither revolutionary nor useful. No-one should be taught mathematics by someone who marks plus and minus infinity with dots on the real number line.

Nurse Dragonbreath
I believe Ray Lashley (way down the list) comes closest to the solution of this mystery. BBC is "pulling our legs". They wave this 'Crazy Doctor' with his flawed math in front of us in order to provoke reactions. And we go straight into the trap! I'm not sure it was BBC, but I'm sure it was some Brittish channel which, a few years ago, aired a kind of 'game show' having people who slept on the streets as participants. The contesters were made to accomplish various humiliating tasks like trying to build shelters from cardbord boxes and other junk. Those who did not win (in what appeared to be a very unfairly judged contest) had to go back to the streets with next to nothing. This provoked an outrage from viewers who phoned and wrote to the TV station saying 'you can't do this to people' etc. Actually, it was all a scam, aimed exactly at provoking this kind of reaction. It felt good then to see that people reacted against the 'game show', and (since I bet this is a similar case) it's good now to see that people really care so deeply about math. And by the way; I think I solved these math issues last night, if you just care to read on. What we want is a definition of the limit 1/x as x approaches zero (currently math defines this value as NOT limited, but rather as 'growing without bounds' iow NOT existing, iow indeterminate. But I have the solution! let x and y be arbitrary postive reals, so that y

Mathew Peet
Zero divided by Zero should be a number on the number line. It has to lie somewhere between minus infinity and infinity, (including 0). For approximate values of 0 perhaps there are solutions. For real 0 the answer has to lie everywhere. It would be more useful to think of the answer as 0 +/- infinity. Or indeterminate. Thanks for this story it was useful mental exercise :)

I agree with Rob. Debating and deciding whether or not this theory is an important task, but more importantly, why is a theory that hasn't been fully proven/reviewed being taught to our children? If this theory proves to be wrong, would you like to know that your children will never understand higher level mathematics because they had this theory inbedded into them at such a young age? Also, at these ages, children take information like this as pure 100% undeniable fact without much secondguessing at all, by the time this is proven one way or the other for sure, it will be ingrained in their heads too deeply to remove, for most of them. -- Papersnowman

Anyone who has even just completed basic programming knows about "null" and thus this is not a breakthrough.

This is weird. This is not dividing by zero, it's just like saying 0/0=x. X could be anything. I'm a sixth grader in the US, and this is just plain stupid, even though I don't understand the comments above I can see that they point to nullity being inconsistent. Setting a variable for 0/0 is supposed to be revolutionary? I think not!

wow. this journalist should learn more about a subject before reporting on it. he/she acted like dividing by zero could actually work. "nullity" wouldn't work because its not consistent

>>"Right or wrong, it always surprises me how many people are willing to be pretty nasty to someone who's come up with a different way of thinking. Why is it so personal to people? Why do people insist the other person is stupid?" The reason it angers people is because Dr. Anderson didn't even try to prove the consistency of his number system, let alone get it published in a reputable math journal. He just contacted the press to get his 15 minutes of fame. This is very frustrating for people trying to do real mathematics, who have published extensive articles on why this makes no sense and yet get no attention whatsoever from common people. Now mathematicians laugh at him (and rightfully so), which just reinforces the layman viewpoint that science is a big conspiracy that rejects criticism and alternative theories. Yes, mathematicians are perfectly right to be angry and to take it personally. If he wants to be taken seriously, he should publish a paper on it before teaching it to a bunch of grade schoolers.

Wrong, his "solution" is like saying: one can get to the other side of the universe by going faster than the speen of light. It's nice to say, but doesn't mean anything at all.

A. Cummings
I'd like to point out that 1 divided by 0 is not infinity. Dividing by 0 is actually an illogical expression because 0 doesn't have a value. For a division expression to be mathematically logical the denominator needs to have a value.

If professor can explain to us all what is the new number then yes he solved the problem. Until then the only think he proved is than the 0 in the power of 0 equals with 0 divided by zero.

So... if I am looking at this right... zero is nothing... it is already just a place holder. You really can't multiply by zero because you had nothing to start with. Just like you can't divide, because you had nothing to start with. If you assume that one of nothing is nothing, then no parts of something is nothing. There I divided by zero. Not infinite. Just not existant. Maybe the answer isn't dividing by zero but getting rid of the place holder and embracing the nothingness. And how to represent nothing? With nothing. Just a thought... one that got me detention in grade school for being "insubordinate".

One of the *first* things he does on that whiteboard is wrong: 1/0 is not and should not be defined as infinity. It can be either infinity or negative infinity. Graphing f(x) = 1/x makes this obvious, or you can try this: Consider 1/x. Let x be a positive number, and shrink it towards zero. This is like approaching x=0 on the aforementioned graph from the right side. The result grows towards infinity. Now let x be a *negative* number. Now 1/x approaches *negative* infinity! 1/0 can be considered either infinity or negative infinity, depending on what the math is being applied to.

He is introducing a new element and he doesn't even define a new set. He uses multiplication of the old set without prooving he can use it. I wonder if he proove the possiblity to introduce this element or if he just use it without thinking of consequences at all? Poor pupils if he teach such theories without prooving them!

Oxford Mathematics MSc
Jeremy Lundy, it is not inconsistent to have nullity = e^(-nullity) in this model. Take for example the fact that a*infinity = infinity when a is a real number. This does not prove infinity is inconsistent when infinity is defined in the way by Anderson here. Also think about a*0 = 0. I very much doubt whether nullity is going to be of any use, but the mathematics doesn't seem to be inconsistent to me.

Many of the education majors I went to college with were in Remedial Math. Apparently some of these have developed their own mathematical style. But if giving a particular kind of indeterminism a name proves to be a useful pedagogical crutch, why not?

Dr. Anderson saying that 0/0 is a number is like saying that an egg is a number. Would he like to define what he means by a number?

Pennywise the Clown
Two things: The theorem T81 [(a*b)^-1=a^-1*b^-1 : a=/=0 and b=/=neg] needs to be an axiom, because the axioms don't seem to justify the guarding clause. Plus, this means that before, division by zero was not allowed, now with division by x*0, x negative, I can't use T81. What's the big gain? It seems this only complicates things.

As a 2nd year maths student I was very excited to hear about the possibility of dividing by zero. But it turns out that is not what's happening at all. Now I am disapointed, but my heart warmed to see so many people pointing out all the flaws so I don't have to.

Andy L.
Since Dr.Anderson will be answering questions later today, here's my first question. 1) Given that the even Gentzen's system for his consistency proof for Peano Arithmetic is itself not been proven consistent, how can you be sure that the Essex Dr.'s mechanical proof of the consistency of your system is anything but hotair?

Matthew Hare
Right or wrong, it always surprises me how many people are willing to be pretty nasty to someone who's come up with a different way of thinking. Why is it so personal to people? Why do people insist the other person is stupid? He's either right or wrong, or he's right in a certain field, and wrong in another field. But do people actually need to get personal about it? Who are they? Are they great minds? Or do they just think they are great minds?

What's wrong with creating a new concept of Nullity? It may help out like "i" did (imaginary numbers, sqrt(-1), etc.) in the understanding of previously unsolvable concepts.

I really think that this new theory may actually help people and save alot of money, time, and even lives. Also I have seen alot of negative feedback from people just because they dont understand the idea and they think its preposterous. Open your minds. You should at least give Dr. Anderson a chance and comment on it later on.

Jeremy Lundy
Using his defintion here is a proof that shows nullity isnt consistent: Assume to the contrary nullity is consitent. Let x=0^0 = nullity lnx = ln(0^0) lnx = 0*ln(0) lnx = 0*(-infinity) (since its a point be his definition) lnx = 0*(-1/0) lnx = (0/0)*-1 lnx = nullity * -1 x = e^(-nullity) Hence: nullity = e^(-nullity) This is a contradiction. Hence nullity isnt consistent.

So, lim(x->1) (x-1)/lnx can be evaluated using L'Hopital's. It yeilds 1. Or, if you don't know L'hopital's, look at a graphing calculator and find the limit of the function as x->1. But, by direct substition in the limit we get 0/0 (one of the indeterminate forms for L'Hopital's), so the limit would be the nullity symbol- no need to apply L'Hopital's if we have the "number" by direct substitution. As math should be consistent, apply the transitive property. We now have that "nullity" = 1. Well, it equals 1 for THIS problem, we could, of course, make it equal any number of our choosing by changing the limit problem (multiply the x in the numerator by your favorite number). Or, consider the structure of division related back to multiplication [6/2=3 because 2*3=6]. If we do this for 0/0 we have the following: 0/0=? becomes 0*?=0. Any number could be filled into the question mark (which is why undefined is an appropriate response to 0/0). Thus, if we are to have a word or symbol for 0/0 or 0^0 [the same thing by exponent rules- which is why we have a^0=1, if a==0] then "nullity" isn't a good one. It should be "everythingy".

T. Vuk
I agree with Dr Noisewater.

how is calling 0/0 "nullity" any more useful than simply saying it is undefined?

Indeed, he's also making the assumption that all infinities are equal.

Andy B
I had him as a lecturer for computer graphics, and he explained this to us. I followed what he said and came to agree with him that something divided by zero is not "on the number line". Big deal. Computer Science, and many programming languages, already use NaN - Not A Number. Heck, I didn't think Infinity was a number either - certainly, I can't represent it as a binary number... Also, having just come from a Control Theory lecture I was annoyed by the whole 'number line' business - every Cybernetics undergrad knows you can't really have numbers without imaginary numbers - so it's all a plane anyway. ;op Still, some of the abuse here is unwarranted - I thought he was one of the better Comp Sci lecturers, and clearly very bright. Like some comments say, though, I did think 'big deal', and he isn't a mathematician.

s squared
If Dr. Anderson is reading these comments: I would like him to elaborate on how his system differs from IEEE flaoting point standard's NaN, +infinity and -infinity.

I don't really think we can do anything with 'nullity' yet. It's just another name, really. But what is useful is the idea of numbers off the number line. If we can figure out more nubers like this, maybe we will end up finding a whole new number line, and find out how to actually use 0/0. It's the concept, not the current usefullness, that's important.

Shanna Wilcox
So I can see where he's coming from. Technically we do not know an exact value for infinity, but when you devide by infinity you get the approximate value of zero. Therefore I am beginning to believe that if you devide by zero, "nullity" you would get the approximate value of infinity. That just makes sense to me...

Bill Gough
Very interesting the level of anger generated by a useful idea. We certainly know from family dinners how much insecurity (or its mirror image - smugness) determines a matching level of anger. I've read postings suggesting that a thinker be 'flogged' and others dismissing postings because of 'language' This new symbol, no matter what its application in math, is proving to be a fine generator of class-bias and racism. Hmmmm - might be something to this concept.

James Lanigan
I am an aerospace engineer and I agree fully with his theory. You guys don't know the history of math. You just believe what the math community wants you to. I know the history of math. Now if Gene Simmons was teaching this, I would believe it.

Dr. Anderson wrote a reply waay down somewhere explaining that he has formally axiomatized trans-real arithmetic, and that it has been proved consistent. While it is easy to come up with contradictions using Nullity and ordinary arithmetic, I am interested to see his axioms. It may not be an incredible discovery, it may be an interesting system to work in if it is consistent. Please give details.

Dr. Limey
Too complicated to teach the whole world this new theory. We should ignore it.

Most of the posts here are just stating the incorrectness of Dr. Anderson's work, but none of them give a truly rigorous proof of the inconsistencies. Due to Dr. Anderson's agreement to comment on the criticisms of his theory of 'nullity', I thought that I'd give such a proof for him to comment on. Hopefully, the BBC will retain the formatting of my post as it will probably be difficult to read without the necessary white-space. We start with some definitions. In the video provided by the BBC, Dr. Anderson gives the definition of infinity to be 1/0. In a post on this article, someone posted as Dr. Anderson (I will assume here that this is actually Dr. Anderson) and had this to say (he implies this in the video as well): "It is just an arithmetical fact that 1/0 is the biggest number there is." So, to put this in rigorous mathematical language, we have the following from Dr. Anderson: 1) infinity = 1/0 2) infinity is an element of the Real Numbers (hereafter denoted R) 3) R is bounded above by infinity We also know that R is a Field and 1 is an element of R. To show that Dr. Anderson's proof is fallacious, we will show that one of his base definitions (infinity) leads to a contradiction. Let infinity be defined as in 1), 2) and 3). It is also given that R is a Field with 1 an element of R. From the axioms of a Field we know that for every a and b in R, a + b is in R as well. Thus, infinity + 1 is in R. But, by the usual ordering of R, we have: infinity

Steve Jay
Once upon a time we had no number zero, then the Moors showed the Romans the new number they'd invented, and book keeping break-evens got a lot easier. This is no more controversial than that, really.

Edgar Matias
This problem was solved in the 1960s by Abraham Robinson, a Mathematician and Logician. Using mathematical logic, he proved that you could extend Calculus to included "infinities" and "infinitesimals". He called it Non-Standard Analysis (Google it/him for more info). Basically, he defined a set of numbers called Hyper-Real numbers, that included all Real numbers + infinities + infinitesimals. Any true statement using Hyper-Real numbers is also true using Real numbers, so long as the infinities and infinitesimals cancelled each other out in the final answer. So, instead of dividing by zero, you divide by an infinitesimal number. You do all of your equation manipulation this way, and as long as the final answer isn't infinite or infinitesimal, everything is fine. It's a shame more people don't know about this. Much of basic Calculus was originally invented using reasoning similar to Robinson's. His work just legitimized those approaches, making them valid proofs.

It is amazing that the real problem with infinities is not even discussed. The result of division by zero is not a simple number. Why? When you divide by zero you delete information. Precisely you delete the information what was divided. All numbers devided by zero result in infinity. The problems start applying equality to infinities. In almost all cases this is not correct, because infinity simply has no identity. One infinity in not the same like the next infinity. Undefined is not wrong, but it goes to far because you can still determine attributes from the infinity e.g. when the infinity result from dividing a number by zero the resulting infinity also has the nature of a number even if it is not finit. Try to approximate the division by zero dividing with numbers like 0.1, 0.01, 0.001, 0.0001 and so on. If you devide the numbers 1 and 2 this way, you notice the result growing. The equations are 1 / n and 2 / n. It is clear that (2 / n) / (1 / n) results in 2. But using infinity you cannot say 1 / 0 = infinity and 2 / n = infinity. But infinity / infinity must not result in 2 because it has less information than the source if the infinity. The quotient of such infinities must be a number, but you do not know which. Unknown numbers are represented by variables, normally. You also can represent infinites by variables to distinquish them. Using phi for a number ist just a variable without a useful name. You're unable to reference that number. Maybe in some cases you do not need a reference. But you also have no further benefit for your calculations.

Brian Fantana
Sorry about my dangling friend's assorted rambling, but Dr Noisewater is very hard to keep pacified these days.

S Squared
You write that Dr. Anderson will answer questions about his theory of 'nullity' on Tuesday. If so, and he reads this comment, can he please go into more detail about how his system differs from the IEEE floating point standard's NaN (Not a Number), +infinity and -infinity.

Dr Kenneth Noisewater
I would like to know why he didn't present this 'solution' to some high level Math students. Oh, but I already know the answer, because they actually understand complex mathmatics. This doesn't solve anything programming wise, you might as well assume that 'nullity' is synonymous with 'error'. If you're dividing by zero in computing, you're generally doing something wrong. What exactly are computers supposed to do with 'nullity', and where are it's practical uses, other than another name for something that is undefined.

Ok first, one cannot define infinity = 1/0 because 1/0 is undefined (and dividing by zero is what he's here to define). What infinity can be defined as is: infinity = 1/n as n approaches zero But fine, we can pass that up. In his proof, he has: 0^0 = 0^(1-1) 0^0 = (0/1)^1 * (0/1)^(-1) 0^0 = (0/1)^1 * (1/0)^1 STOP Right there, he has an indeterminate form, 1/0 is undefined, this line in the proof has to be true in order for the result to be true. But, he gets around this because he has defined 1/0 = infinity, which is all kinds of wrong.

This is why we have try{} constructions. Why would 'nullity' be useful? I see no reason that nullity would be better than NaN.

There was a rumour that a U.S. State in law defined PI = 3.0 Such definition, fortunately, did not make it so.

This is a silly idea. Computers cannot handle "nullity" any more than they can handle "N/A" for 0/0. Error checking will not be replaced, it will simply be misnamed, and more errors will come as a result.

I absolutely understand it. When will this be taught in schools around the world. It fills a large gap of understanding when studying Calc.

What? Is this satire? If so, it should be clearly indicated instead of presenting this as some sort of credible concept. And if not, is there no one at the BBC familiar with mathematics who can review these stories? Or at least contact an expert in the field or at least a local professor before publishing garbage like this. BBC, you should be ashamed.

hey, some of you people bother me. how many of you have said "1/0 = infinity" here is why that is NOT true: 1 = 0∞ = (0+0)∞ = 0∞ + 0∞ = 1+1 = 2 see, it doesnt fit real math if 1 = 2 anyway, all that this guy is doing is making a symbol for this indeterminate result. instead of just writing "not real" or "indeterminite" he decides to make a little symbol for it. as far as i have seen it has no implications beyond allowing computers to not freak out when one divides by zero

This doesn't solve any problem related to Computer Science... Computers don't inherently know how to divide (or do anything, for that matter); they have to be taught - someone has to design the circuit for division, and figure out what to do in the case of divisor=0. In most cases, an exception is thrown or an error flag is set; however, I've never heard of a system shutting off when dividing by zero (and I *highly* doubt they'd program a pacemaker or autopilot to shut-off in that case).

Jason, the reason 1 is the limit is because its a definition; made up because it suited our purpose. dont think your argument is accurate, same for many other of you people. In any case, I am not sure Dr Anderson has actually given us anything we can actually implement.. but nice trying..

I am glad that BBC wrote about this. I never knew this was a problem, but by reading about Dr. Anderson's theory I found the solution myself. And I am not going to reveal it here :-) Dr. Anderson's theory is wrong. That much I can say for sure.

I am an engineer .. i didn't understand what did Dr James Anderson came up with but it's something amazing !!

In computer programming we take hand of dividing by zero as a separate event in where series of calculations. How this event will be taken, will be decided by programmer during analyzing the environment in which the calculation serie is doing. As I know, the right decition will be done if division by zero occur. Therefore there is no occasion to be afraid of something going wrong in autopilots in aircrafts, and in pacemakers.

There is nothing new here. What Dr. Anderson has done is to take those operations, (in the reals or extended reals) which result in nonsense, (in the usual sense) and use them to define nullity, (specifically those cases which are not handled by the extended reals). To summarize, we now have a new word for undefined. P.S. What happened to the co-authors of Dr. Anderson's on this subject? (See the academic papers on the subject: Perspex Machine 8 & 9).

Ste Millington (Software engineer with Pure Maths
What is the point of a computer happily churning away calculations involving division by zero without any errors only to find that the results don't have any meaning? I personally wouldn't like to be on a plane operating with Dr Andersons new arithmetic when because of some programming error a division by zero occurs and the navigation system carries on regardless - giving us a position of nullity by nullity! Dr Andersons axiomatisation of his new number system does appear to be consistent (given a cursory glance) however it's just plain useless! The point is that in the real world if you are trying to divide something by zero you have made a mistake and any well written computer program should handle these errors effortlessly. In Dr Andersons new system we gain the ability to perform division by any number upon any number, but at what cost? Well to start with we can no longer infer that because x + a = x + b then a = b. This is such an ingrained and natural notion that adopting the new number system would inevitably lead people to error. Though sickeningly grandiose in tone Dr Anderson's first paper does at first glance appear at least to be consistent within in its own bounds. Fine. His second paper on calculus exposes a clear lack of mathematical training and is flawed in many places. I would be amazed if any peer reviewed journal would consider publishing either paper.

Matt P
This looks about as useful as complex (or imaginary or non-real) numbers in that in conventional and most applications, it is entirely useless, a mathematical definition with form and no subtance. (finishing year Calculus student)

Suspicious Cricket Fan
I am indeed very suspicious. It seems as if this whole theory has been invented to somehow apply some formula to the impending Australia 5 England 0 result in the Ashes Tests to provide a "mathematical" possibility of England retaining the Ashes despite sending out a second rate foreign legion XI who play like crap.

Eric Mill
Dr. Anderson should get in touch with Dr. Stephen Colbert, an equally renowned logician, whose concept of "truthiness" has been getting an amazing amount of press.

We all know that it's impossible to divide by 0... but is it impossible to MULTIPLY by 0?

Sorry, but could somebody please insitute a national programme to teach people spelling and grammar? I realise some of the posters are not native English speakers, but the majority of the rest need to have something equivalent to national service to help them learn to communicate. Once that is done, perhaps they could try learning some mathematics and, in many case, computer science.

One of the most beautiful example of the stupidity of the journalists. There are tons of real astonishing scientific breakthroughs that we never ear about because too hard to understand for the quasi totality of pseudo scientific journalisms we see on televisions and web and hear on radios. This non-problem is very trivial to demonstrate to pupils 0.001^0.001=0.9931 0.0001^0.0001=0.999079 0.00001^0.00001=0.99988 0.000001^0.000001=0.999986 Even non mathematicians see this converge to 1 : then 0^0=1 This is not because your computer does not work due to poorly implement code that you should think that there is no solution. Why need to create absurd symbol for 1? Please Please journalisms of the world, the best thing you can do when you have nothing to write or say it to shut up and take vacations, don't pollute our medias. One thing I can recognize here is : they are qualified to speak about nullity , even infinite nullity :-) And to finish most processors know what to do to divide by 0 , but the programmers need to pay attention to this detail and treat an interrupt or the Nan or Infinite number they will get if they divide by 0

Jason's resoning is faulty, as (1/x)^(1/x^2) goes to infinity as x->oo even though it approaches 0^0. The point of 0^0 in a calculation is "how" one is reaching the limit. The "nullity" has been around in computer science, most math processors have a special "number" NaN, which stands for Not a Number. The result of 0^0 is NaN, which this professor calls nullity. Nothing to see here, move along!

I suppose this could open up new branches of theoretical physics, but in practical application, it's pretty silly. Still I suppose this is no worse then when 'i' was assigned the square root of negative one.

Can you define a word, by using that word in a definition?

And here I thought dividing by zero was infinity...

0^0 is indeterminate, but if you take (1/x)^(1/x) as x gets very large is essentially 0^0. However, this limit is 1, not this "new number" nullity. It is called indeterminate for a reason stop wasting these kids time!!

Let's go back to the development of the rational numbers. Two theorems. 1) For any rational number z, we have that 0*z=0. 2. For x,y,z rational numbers, we have that x/y=z if and only if x=yz. Now suppose x/0=z for some rational number z. Then by the second theorem, we have that x=0*z. So by the first theorem, we have x=0 and our original equation x/0=z becomes 0/0=z. Now we have by the second theorem again, that 0/0=z if and only if 0=0*z. But this equation holds for all rational numbers z, by the first theorem, so 0/0 could equal any rational number and thus is indeterminant. This is why division by zero is not allowed, unless, you suggest those two theorems are incorrect and thus are questioning the whole development of the real number system.

This is ridiculous. It is a disgrace for BBC to even have it in the news. This guy is not solving any problem because there is no problem. Even infinity is a matter of definition. You can give 0/0 any name you want, there is nothing magic or smart about it...

Kate Monday, Mathnet
The idea is neither novel nor 'outside the box' - this is something plenty of mathematically curious adolescents do upon learning calculus. The reason no one has previously bothered publish it is because 16-year-old calc students generally grow up and, if they stay in math, move on to deeper and more significant areas of study.

I think it is perfectly logical and necessary. As a computer science person, the ability to do this is priceless. And using nullity makes perfect sense.

i get where you're coming from, and if math is always equal and such, why isn't that possible????? so like if i got to understand it, yeah, im sure it would make sense and stuff, but right now im just a kid with no idea about it, but it sounds interesting. im inspired that someone could find a mathmatical solution for that though! lol :)

The theory of calculus
"But Dr Anderson has come up with a theory that proposes a new number - 'nullity' - which sits outside the conventional number line (stretching from negative infinity, through zero, to positive infinity)." Well gee, maybe Dr. Anderson should finish his course in math before he begins teaching it. Let's see him count from negative infinity to zero, to positive infinity. Or rather, devise a method of doing so.

While he has every right to create his own axiomatic system, if I recall correctly, the conventional system has an axiom that you cannot divide by zero.

Kevin Rollins
Oh boy, this is just setting these kids up for failure if they ever reach higher mathematics. Calculus deals a bit in indeterminates like 0/0. You need to recognize that it isn't the real answer.

Isn't it kind of silly to label a concept "revolutionary" when everyone's already thought of it, and simply discarded it because it's not anything new-- it's just that we've chosen not to work under this set of rules? If you want to invent a new axiom system, whatever, go do your own thing, but it's really goofy to pretend that it replaces the usual system and makes that system inferior because "no one's ever thought of your concept before." Um, everyone's thought of it; they just choose to work with the usual set of axioms because there's nothing in their work that makes "NaN" a particularly interesting thing to work with. I think taking limits is a much more interesting idea than just slapping a definition on something that can't live in the real number line. At least we can work with limits and do neat stuff with them in the axiom system we've already made so much progress in. Who wants to start over?

In his introductory definitions he states that 1/0 = infinity. Then in his fourth step he is multiplying 0 or (0/1) by infinity or (1/0) [see definitions, positive infinity = 1/0] which would result in the answer being 0 or [0/1 x infinity = 0 not 0/0 or "nullity"].

Dr. Viktor I. Planckenstein
There are some very interesting things about zero, and triviality. First, "The Existence of a Trivial is Indeterminate". This is very important and easy to prove. It says that you cannot prove whether an object is really itself, or if it might in fact be an identical clone of itself. That this is strictly "indeterminate". This is also true of numbers, etc. This is Harris's Theorem, and is perhaps the most important theorem in all of mathematics. I'm not sure if nullity is the same as a trivial, but it might be. I am not familiar with what this man is doing. Next, when are apples equal to oranges ? When you have zero of them !! Yes - indeed - zero apples is identical to zero oranges. There is no difference !! Triviality is not a trashcan. There is a distinction between the trivial and the strictly nonexistent. If this man is teaching nonsense to schoolchildren then he should be flogged. But if he is investigating the idea of triviality then I'd say he should get a medal. I think that I'd need to see his math first before making that call. Is an apple the same as an orange ? Yes, when you have zero of each !!! An apple is an orange !!! I am not advocating division by zero, but there is certainly MUCH to be said regarding triviality ! Respectfully, Dr. Viktor I. Planckenstein

Nathan Bixler
No offense to him or anything, but I devised a way of doing this last year out of sheer boredom. THe fact that no one else has ever done this astonishes me. Also in my case, I used an L (the pound sign) as 1/0, and did all my math from there. But seriously, its not that inventive.

This makes no sense! Why doesn't the station realize how many people have a problem with this and let the professor know how wrong he is?!

if(x!=0){ z=y/x } Are my maths revolutionary?

The dimwittedness of most of these comments posted here is wonderful. The people who are trashing this article don't even seem to have a rudimentary grasp of language, making your claims to have any understanding of the language of math laughable. To those of you who posted comments like "the BBC should publish an full apology," and name-calling like "marons," thank you, you've made my day.

X/0 has to be infinity. Infinity not being accepted as a real number by mathematicians, neither number being acceptable, and any number greater than zero leading to any value less than infinity, it leaves no other choice, unless we want to create a number greater than infinity, heaven forbid. The question is reversing the formula where then 0*infinity is X, but of course zero multiplied by anything is zero, real number or not. Is it really that hard to accept the idea that there's one method that's irreversable?

Actually, 1/0 can be regarded as infinity in extended real number system (consider, also, the Riemann sphere). Naturally, this does not excuse Dr. Anderson's theory from being totally useless -- as others have pointed out, this is essentially a redefinition of NaN.

ofc we can divide by zero. At least in theory.. short course into known (not so well known, seems)three dimensional numeric system: "first" dimension: real numbers - including (positive/negative) infinity and 0 (based on 1) "second" dimension: complex numbers - includes real numbers. There we have so called real axis and imaginary axis (constituents are 1 and i={square root of -1} ) *about those 2 dimension there are plenty of definitive works available for everyone "third" dimension: That seems exact place for nullity (call it however you want to). any complex number divided by zero belongs to third dimension, which includes both first and second dimension Constituents are 1, i and 0/0. It's an extension to complex numbers 0/0 ~ a, where a is complex number (so basically 0/0 is complex level) however a*(0/0) does not equal (a*0)/0 = 0/0, because 0/0 is base component, therefore |a| is "heigth" of 0/0. But projected to complex level a*(0/0) DOES equal (a*0)/0 = 0/0 = 0 (real number) if a is negative, then a*(0/0) is located below complex level if a is positive, then a*(0/0) is located above complex level. about x/0: as most of as know - x/0 tends to be infinite. in upon described three dimensional numeric system x/0 equals (0/0) times infinity (infinity, as it is in "second" dimension) So x/0 is a "border" of "third" dimension (where x is complex number) well, as english isn't my first language AND it's 3:30AM here atm, i apologise for any mistake i did (either linguistic or mathematical). Need some sleep tho. If requested, i can explain it a bit closer tomorrow.

crap, ive been discovered

a physics proof
ok this might go over some peoples heads but hey..... In relativistic physicswe can define engery as E =(mass x c^2)/squareroot(1-speed^2/c^2) which if the speed = c and the mass =0 comes out as E= 0/0 which acording to this guy would be equal to nulity which acording to him is a number that does not exsist in the normal number line. but the speed and mass of a photon are indeed c and 0. and a photon does have an energy defined by E=h*frequency which is a real number. the point is 0/0 is simply undefined thus if E=0/0 by one equation it could still be defined by using a different equation. Im sure theres a mathematically allegate way of say this but basically as the OS guy pointed out 0/0 can have any value. so to say it is a number that is not on the number line is most deffentally wrong and it is indeed scary that this has been made news worthy as a piece of mathematics. maybe its usefull for computing but its tot maths

Ahh man I was just getting trigenometry. Now we have to add an extra grade to study something that's not there.

A.R.Yngve, Sweden
Years ago I wrote a science fiction novel, ALIEN BEACH, in which the solution of "1 divided by zero" heralded a great scientific breakthrough of virtually transcendent proportions. I wasn't really serious about 1/0... and I never expected a solution to come true, either. But once again truth proves stranger than fiction, eh? ;-)

Oliver, 17, IB Maths Higher Level student
I laugh but I cry at the same time. You step outside of the classroom and *wham*, you see how stupid the majority of your country is. Shame on the BBC, they have just given me the only excuse I need not to pay my licence fee and switch to intelligence-powered media such as slashdot and b3ta. Oh Lord, "Could your maths knowledge be divided by zero"? It wil do no such thing you hacks, but you have just proved that bbc.allknowledge = 0

The Godfather
The italians have known forever that nothing divided by nothing equals nothing! A big FAT ZERO! What is wrong with people! SHEESH!

The important question is: why is an unproven theory being taught to school kids? I don't think much of this theory myself, but that isn't the point. Even if it was the best thing since sliced bread it should still be peer reviewed and then added to the national curriculum before pupils get to see it.

Hmm, this is very strange. I don't think he is right. I guess you could get a symbol kind of like i that signifies something that couldn't exist, but then much of differential calculus would be proved wrong or trivial if this were doable for n/0. It could work for elementary math, but I think it does not apply to advanced mathematics.

Thank youy, this is truely interesting. It wil take math to a whole new level. One down poit: Many childern will hate you for making their homework longer and a tad harder. The rest of the world thanks you.

I think it is not just ridicoulus, it is offensive, I can't believe that this kind of people were teaching, I would like to know where did he study and check his title. Did he realize that were confusing some children?

Hmm, sometimes I think people how post such scathing remarks are not even mathematicians themselves, while I also disagree on the argument at hand, it is not however right to attempt mathematics when some of you appear to have no idea what math is also. for one thing, the complex number plane does not exist in the real number plane correct? The complex plane only exists when written down, hence why its the imaginary number plane, I believe some of you would ahve trouble thinking in more then 5,6, or even 7 spatial dimensions or thinking that certain subspaces are purpendicular to themselves and to every other number out there...some of you who dont know this might want to learn some Linear Algebra at some point and maybe you will gain some understanding before you make comments. Though I dont find the problem to have been solved by creating a new variable myself. It seems lacking anyhow in substance.

Hi im in yr5 we dont do that in my school we do fractions and shapes and that

The moral of the story? journalists (arts graduates) should not be allowed near science stories.

Tony Hendrix
Does he not realise that when programmers write code - especially for essential purposes like pace makers they will check if division by zero is occurring?

Asaf Reich
Great. So now a pseudomathematician can go around proving he's practically a mathematical Messiah ("It's that easy!") by teaching it to tenth graders. Wonderful. I don't suppose this report could have been sensible enough ask a mathematician about this, nooo. That would have been far too...logical. Unlike this theory.

Alexander Poindexter
The very idea of putting something that is beyond the third dimension into the views and constraints of the third dimension is the same as telling a baboon that you are it's father/mother and that it should act more human: absolutely absurd. We are limited by the three dimensions. To reach beyond that requires a thinking that extends past the 10% of the brain that we use. The last time I checked, this mathematician doesn't appear to have transcended our conventional way of thinking. And for him to shove that kind of thinking onto high school students shows no humility to the other established and more well known mathematicians in the world... I don't even have a degree in mathematics and I can see through this area of thought.

Personally I think it's rather pointless. The article claims that not being able to divide by zero could cause major problems, even fatalities, but here's the thing: How often does this happen? Personally I have no idea, but my own guess would be that it happens extrmeley little, if at all. But beyond that, how can you just create a new number which will solve one problem, without creating a set of it's own problems? For example, what happens when you try to divide by nullity? And back to the whole computer thing, even if it does encounter an error, would it just shut down? If you programmed it to work with "nullity" (There's another problem, you'd have to upgrade existing technology to even recognize this new "number") then what does the computer do with it, just say "Oh, alright, moving on..." Why not just make it do that with the error? It all seems rather pointless to me, and even absurd to make something up to answer a question.

Here's a thought. If I have x sweets and want to share them out to y people including me, each person gets x/y sweets each. But if I have x sweets and want to share them out to no-one, not even me (out to 0 people), what happens to the x sweets? Do they collapse on themselves as they nullify their own existence? I think not.

Guys, I think a lot of you are missing the point, the guy is a COMPUTER SCIENTIST, not a mathematician. He's come up with an intuitive solution to a serious computer problem. Does it matter if it's the real for true solution if it works? The answer is no.

Not a math person..
I'll admit this thing has me confused. But then so did i when I learned about it in math class. The only thing I can say aboout this is Old Albert Einstine was also ridculled.... for E=MC2... least till they split the atom.

Wait, I can figure this one out... Okay.. So, nullity is--*Matrix explodes*

The X
I am really against this. Proposing to make a number not on the numberline is ridiculous

Well, this problems hasn't gone un-challenged before, and this supposed solution leads me to say that this teacher should just stick to the syllabus. The understanding as i and my friend came to was that it was incomprehendable, and we came to the agreement that the solution to the problem is "possibility itself".

The absurdity makes me laugh ...
Taken from Mr. Anderson's paper: "Having capital Phi lie off the number line blocks the counter-proofs from real analysis that attempt to show that 0/0 is undefined." So basically, you're saying since "nullity" lies in its own unique universe; thus, it can't be disproved by any known mathematics. Gee, I didn't realize I could do that. In that case, I better inform my math teachers that I deserve all A+'s, because all my answers (even the wrong ones) conform to this new mathematical universe I invented jsut today where my answers are always correct.

El franco
The solution is wrong, there are no infinity, you could always add 1.

It"s wonderful!Dr. Anderson has shown the infinite and the negative infinite impact on zero and given it a new name. From now on those who do not understand the theory of nullity will forever be called nullidiots.My husband is the very first.

This just goes to show, if you get enough people to back you up on something... IT WORKS! Why? There just needs to be enough people out there to go along with you, and then it doesn't matter what anyone else says. Doesn't math already have enough crap involved?

You scientists who are bashing this development don't quite get it do you? It takes an computer engineer to see the potential here. By creating a "magic" number that REPRESENTS division by zero, all sorts of fault tolerant computing can be performed that wasn't possible. He uses that example in his statement, and I have come across fatal computing errors due to zero division many, many times. Instead of requiring programmers to ACCOUNT for zero division, we can develop computational engines that can deal with such an operation. Keep arguing about abstracts you math geeks...this is why I get paid way more than you...

Shame on you BBC next time you publicize something about math, make sure that YOU don't understand it

Well this isn't quite as silly as you might think from the article - he hasn't just assigned a symbol to x/0 (which as people have rightly pointed out is no different from NaN etc) but is proposing a set of axioms for 'transreal arithmetic' in which 'nullity' can function as just another number. No of course nullity doesn't 'work' as a number on the real line, but on the proposed set of extended reals it would. The aeroplane/pacemaker thing, however, is obviously ridiculous.

Derek Andrews
This does seem to be stirring up quite a hornets nest and it makes me wonder if the programmer who set this page up gave any thought to what happens if there is an infinite number of comments.

Just reading through the comments and it occurs to me that it's pretty cool to see so much passion about mathematics. (Okay, I was going to try to be funny by saying " much passion about nothing.", but that would be a discredit to all of you.)

Nullity is awesome can't wait to see this in software.

I asked 'Dr Math' of (proper mathematicians) what they thought, a good summary i think: "Hi, Thanks for writing to Dr. Math. I've actually been waiting for somebody to write in with this very question. No, Dr. Anderson isn't coming up with anything new. Yes, he's missed a few details. It's important to address what he has really done. He hasn't come up with anything new on the 1/0 score. Defining 1/0 as infinity is actually fairly old. The new thing he has developed is defining 0^0 = nullity (and defining 0/0 = nullity). Note that I said "define". Although he claims that it is a consequence of 0/0 = nullity, this isn't true. Some background information: Under the standard real number system (the one we are taught in school), there is no infinity, nullity doesn't exist, and we operate under the math we were taught in school. For some mathematical applications, particularly those involving limits, infinite sequences/series, and some applications in computer science/engineering, we use what is known as the "extended" real number system. The extended real number system includes two quantities we call "infinity" and "-infinity". We define these quantities so that: infinity > a, for any real number a -infinity

I don't understand how this works as anything new. He gave a computer example, so thats what I'm going to work with. "If your pacemaker divides by zero you're dead." It should either throw an exception that can be handled by the software (and either terminate on its own; 'killing the person', or trying to recover), or it should be checked BEFORE dividing it. Now, assume the division returns a special number. How is that pacemaker going to handle that? The same exact way it handles exceptions that get thrown, or an assertion BEFORE doing the division. Either terminate the application or try to recover. Now my biggest question is how exactly is it planned to represent this in a way a computer can understand? Lets assume the number is 1 byte, just for simplicity (this can scale up to however high you want). 0x0 (0) and 0xFF (255) are all taken. How does he plan on representing nullity? All 8 bits are spoken for. In a 32 bit integer, 0x0 through 0xFFFFFFFF are all spoken for (be it signed or unsigned). How does he plan on having a different number come out of 8, 16, 32, 64 etc bits, when ALL the bits are already used. The only way I can imagine is the SAME WAY it is handled now: Throwing off a special exception. You CANNOT just say "ok, 0x0 will now represent nullity". That does not work. Then any math done where the result is 0x0 (what is 2/100?) will return "nullity".

Ari Rabkin
My first impression was that this was slightly kooky, but the great thing about science is, the actual paper is online, and is pretty easy to follow. I think I understand what Anderson is doing, and it makes sense, although I'm not sure I'd call it newsworthy. Numbers don't come from God; we can define them. Normal arithmetic defines multiplication and division in certain ways, and does not define the operation of dividing by zero. It's perfectly possible to tweak definitions to define a nonstandard arithmetic. People have been doing it for years, with complex numbers being the most famous example. If you look at Dr. Anderson's definitions, it is indeed true that 1/0 = 2/0, but no contradiction arises: that statement just says Nullity = Nullity, and multiplying both sides by zero doesn't result in 1 = 2. It's much like the way that sqrt ( 1^2 ) = sqrt( (-1) ^2) does not imply 1 = -1. As a number of people have pointed out, most computer systems already use an arithmetic system with positive infinity,negative infinity, and a special symbol called NaN (not a number). What Dr. Anderson is saying is, "look, if we tweak the definitions a little bit, we can get NaN and the infinities to behave in a more consistent way and look more like the real numbers". Hardly revolutionary, but I can see it being useful in some computer programming contexts.

Peter John Yannone
Mathematics has its limits. It is a finite model that we use to analize an infinite subject. In the real universe, integer values are unachievable; including zero. But integers are quite useful in science and engineering. Zero is better defined as an asperation toward nothingness: as one over infinity. This solves every problem I have applied it to so far.

I would like to know how mr. Anderson defines 0. Seem like he has forgotten to do that in the first place.

Its called the extended reals people: R union {plus or minus infinity}. You can work out an arithmetic, but 0/0, infinity/infinity, and infinity - infinity are still undefined.

The nullify symbol is already used in mathmatics. It is the greek letter Phi and is already equal to something.

I think it's really cool I love Math and would love there to be a new theory to be proved but I don't see how zero divided by zero can equal infinity

George Aylor
Not so fast you naysayers! It was 800 years after the Mayans had the concept of zero before the Europeans caught on. So give Dr. Anderson another 800 years to prove his theory.

I'm okay with this. Much of math is created, not "simply derived by logic from nature." (Much of it is simply derived, just not all of it.) Given the portions that are just constructs: necessities like irrational numbers, why not have a null number that allows us to perform *around* otherwise dead-end operations. Regardless of that, it gives our computers and computer chips an escape method. This is a good thing. We may very well see benefits in our own lifetime.

Jaharashma Atmakandahahr
Why can´t we just agree that x/0 = x, or perhaps x/0 = 0, instead of having something mathematical that isn´t allowed (division by zero) !!! Division by zero is truly a real bug in the mathematical system which still hasn´t been corrected!!!

I don't think it's possible to divide by zero. If Pythagoras couldn't do it, who can?

The axioms in his paper are inconsistent (assuming that infty, -infty and Phi are distinct). 0^{-1}=infty and (-infty)^{-1}=0 quickly lead to infty=-infty (axioms [A20], [A21]) since Phi=infty-infty=infty+infty=infty [A11,A5] we have equality of all three "numbers".

In my country we hunt mathematicians.

MA in Maths and Computer Science (Cantab)
Many people here have missed the point. If you go to his web-page you can see that he has developed an axiomatic system that is very similar to standard mathematical axioms, but slightly different - in the vein of non-Euclidean geometry. He has added the quantities +infinity, -infinity and nullity - really just setting out in mathematical language the rules regarding +/-INF and NaN in the IEEE floating point standard. Unlike complex numbers, you can actually DO anything new with these new quantities (e.g. the equation 0x = 1 is still unsolvable, 0x = 0 still has infinitely many solutions - none of which are infinity or nullity). Teaching children how to reason logically given a different set of axioms is, in my opionion, a good thing. However, to teach them that this is a brave new world and a paradigm shift for computing woyuld be a downright lie!

Jimmy Klavoc
What annoys me about this article is the suggestion that it will solve problems in the real world realm. As far as computers are concerned depending on the language you're using you will either have to check beforehand that you aren't dividing by zero or catch a DivideByZeroError or whatever the type throws. I don't see how making up another imaginary number (just like i and j) helps solve anything practical at all. i and j have been useful, this seems to have no such potential. Seems like someone has lost their head up their own you-know-wheres to me.

Computer Science PhD
Computer scientists are embarrassed by these deceptive claims. The BBC should publish an apology for its cry-wolf reporting instead of trying to spin this as some sort of positive catalyst with provocative or inspirational worth. Dr. Anderson's 'theory' hasn't generated the healthy 'debate' that BBC portrays, it's drawn virtually unanimous rebuke from the public.

This is truly ridiculous. The whole coverage and "idea" is nonsense. I have no idea why this nonsense collection of sentences is being reported on. Anyone with mathematical knowledge shouldn't even go as far to call it a theory or argument - it's just sheer insanity in the form of a few sentences. Perhaps next week you should send your reporter onto the streets one evening to ask the drunk public if they have any more reportworthy ideas.

quirky people do have the right to create their esoteric math systems, even if they wish to rename and refine NaN to feel like they've done something new. but to advertise this as any kind of breakthrough is hubris; to pitch what is in essence a tautological solution as capable of doing something different than NaN in already error-catching pacemakers and autopilots is to sell snake oil; to teach this math to year 10 students and imply that it could ever be a part of normal algebra is grossly irresponsible. 1=2; 1/0=2/0; nullity=nullity; q.e.d. ?? it doesn't even satisfy normal equality. if you want to inspire kids to math, tell them about pythagorean number cults and show them fermat's last theorem.

R.C. J. Weasel
Dr. Anderson's theory leads to some surprising conclusions, such as the idea that either you can't do anything with this nullity, or 1 = 0.

The Cat Baron
(N^0) - 1 = 0 therefore ((N^0) - 1) / ((N^0) - 1)= 0/0 = N^0 + 1 = 2? Sounds just as stupid as what this "teacher" says he has come up with...

1/0 is not infinity. 1/x as x tends towards 0 is infinity. therefore you have based an argument on a false premise. go and try again!

Alix Paultre
This has been needed for centuries, but especially now in an age of inflexible computer minds that cannot fail in operation. Just as "i" represents the square of negative one in order to perform complex math, "nullity" will do the same for zero. Dr. Anderson is a genius.

Dr. Gary H. Kramer
Interesting. The "new" number is really a named error trap. I see no evidence how "nullity" can be used beyond the error trap. Also, the position he placed the number is in the complex domain, so I suppose he's just extended the number plane to another dimension!

Okay.. So he has redefined NaN? Nonsense.

I'll tell you the giveaway: most new theories are peer reviewed before being made public. When you instead decide to present your theory to a classroom full of kids (who don't know any better anyway), it shows that just maybe you suspect the grown-ups won't believe you.

Dr Michael G Koch, Sweden
This is a truely underwhelming solution of a problem that is not. It has been hovering in the air for much more than 1200 years like a brick does not. Thus the best comment is, in fact, that of Albert Einstein (look it up!). Dr Anderson should now, indeed, concentrate on the 2500 year-old problem of negative infinullity which not even Confucius has solved. It was the following line of thinking: Gottlob Frege - Wilhelm Ostwald - Ernst Mach - Rudolf Carnap - Moritz Schlick - Otto Neurath - Reichenbach - v Mises - Ludwig Wittgenstein - Kurt Gödel - Bertrand Russell - Lee Whorf - Karl R Popper - Quine - Morris and modern semantics, i.e., the konventional mathematics and logics, 20th century positivism, the Vienna Circle and the neurophysiologically inspired modern critical semantics, which helped us to escape from the old fashioned idle-running of philosophical pseudo-thought into the pitfalls of language: Why is something and not instead nothing? (Heidegger), What is the meaning of being? Which foot is ugliest: the ugly one or the ugly one missing an ugly toe? (Old Vikings next morning in the Celebration Hall), Who is bigger, mrs Bigger or Mrs Bigger's baby? (The baby, 'cause it's a little Bigger)..., the "liar's paradox", "Achilles and the turtle" etc. So let us just use a little advanced understanding of language: Null or zero was once introduced in India (primarily a tiny central point, then a thick one, then a little ring, later stretching out into a bigger circle and, finally, into a 0, looking for an easy mode to mark an empty space: 1, 2, 3 etc ment that there was a certain quantity of something (people, animals, objects or units of parameters - like m, sec, V, A, mg, km/sec, l or whatever) on a certain place in the decimal system and 0 ment that there was nothing. Now our language permits us a confusing lack of exactness to say both "He stole nothing" and "He didn't steal (any thing)". The difference of these two meanings is detectable by asking: (1) Did he steal? 'Yes' What did he steal? 'Nothing'. (2) Did he steal? 'No.' We have a negation floating around in the sentence and our somehow 'unexact' grammar allows us to put it somewhere. That creates many pseudoquestions, which can bother us of merely grammatical reason: It rains? What rains?? The sky? The air? The clouds? The water? The weather? No - we have just a rule saying that a sentence needs a subject/noun and a verb to be complete. We put a toltally empty 'it' into the sentence to fulfill that requirement. Should we allow our language (as it is in some other languages) to leta sentence be without a subject, we would say only 'Rains!' instead - and the problem wouldn't only vanish but be impossible to put. To divide with zero is nothing else than not to divide. Otherwise one should put people into prison for stealing nothing, though - due to the infinitely small theft - only for some millisecond. The problem here pretended to be solved is not existing for educated people thinking with real exactitude. It is just a question of some sort of 'advanced enlightenment'. Q. e. d. Michael G Koch, MD (open for comments)

Hungry Hippo
I'm not sure which made me laugh most: the original 'theory' or some of the attempts on here to disprove it. I had no idea we were blessed with so many mathematical geniuses visiting the BBC.

`nullity` is actually used by ancient indian mathematicians for dividing by zero.. they said it as `syoonamanak`.. i thik there should be more study about it

His idea of the limit as x approaches 0 of (1/0) and -1/0) is nothing new. phobos puts the correct theory of infinity below. Infinity is not a number and nullity should not be treated as a number. Also, since math is defined for three dimensional space Where would nullity fit. It is definitely not a complex number and would not be in any Mandelbrot or Julia set. Jeff the U.S. citizen with a masters in math is not far off in his ideas. However, if you look at the limit of (1/0) and (-1/0) you cannot leave the abstract method of calculus and its definition of infinity. By your understanding then infinity is just another defined variable where basic algebraic concepts can be applied. This does make sense. However, what is infinity? If it is the largest number possible then (1/0)=(2/0)= infinity. So how can you treat infinity as a variable?

John Killary
Is it not a bit odd that this wonderful discovery in maths has been made by a non-mathematician, verified by two other non-mathematicians and published in journal of the Society of Photo-Optical Engineers. Why is there no mathematician quoted who supports it? Why was it not submitted for peer-review to a reputable journal of mathematics? I wish one of the school children had put this question to Anderson: If 1 x 0 = 0 and 2 x 0 = 0 then 1 x 0 = 2 x 0 Divide both sides of the equation by 0. You are left with 1 = 2 Some mistake here I think.

Me > Dr Anderson
Asking for the answer to 1/0 is like asking where exactly is the EU in Britain. Let's put this another way; 1/0 is asking the question what number multiplied by 0 is equal to 1. The answer: A slap round the back of the head, since any number multiplied by zero is zero... Unfortunately the bbc has asked a computer scientist with the IQ a couple of points more than a stick of butter who's interested only in stroking his own ego by claiming to be smarter than newton etc. Maybe the beeb should check such stories with actual mathematicians before just running with it.

Patrick Killary
The BBC should publish an full apology. This feature is an insult to mathematicians. Would the BBC show Physicist claiming to have made a remarkable discovery in Chemistry without checking with a Chemist? Of course not. Then why publicise a supposed Maths discovery by a Computer Scientist? Did Dr Anderson discuss his theory with a mathematician? Has he ever taken even an elementary course in Algebra at university level? His rubbish would be laughed at in any first year university class. I am a Maths graduate and there is so much wrong with this that it is frankly embarrassing to watch.

this is just lazy journalism- i know nothing about the theory so was very interested in the article- had the BBC done even some basic verfication they would have realised that it's all been done before as has been demonstratedb here- i don't expect them to be experst on all things mathematical but a few phone calls could have stopped them wasting their time with this- v dissapointed that something like this could have made it far as South Today- i mean if they aren't gonna verify facts im sure i could come up with more newsworthy items...

phobos, our dear professor defined them as real numbers and opposite of one another. By his definition, they are the same number. In reality, infinity is a concept and not a number and thus it is not subject to the laws of math.

if 0 is in the exonend of 0 it is not defined..for all other numbers it is 1... or am i wrong? so the start of the "theory" is not right.. how can the end be?
this solution solves nothing! Dr just 'invented' new termin, thats it, nothing special...

I have just reviewed the paper in question and I must say it is a load of old rubbish. In the few proofs he gives he uses his theory to prove his theory. This is like saying "I think the earth is flat, therefore the earth has no curvature, therefore the earth is flat." As I said pure rubbish or a very unfunny joke.

Haha, that's kinda nonsense. I mean, it's a nice idea, but it doesn't help at all, I think. For such problems, you could use L'Hospital, but just if you have functions which result in 0/0. Nullity is not the solution for this problem, it's just a short way out, which doesn't help.

Jo Miller
It's fascinating to see the vehement reactions here. I don't have enough background in algebra to quickly understand his paper, but I do have enough to see that since this is outside the real numbers, normal rules do not apply (sorry folks with your apples and pies). It may or may not be nonsense, or useless, but I don't have enough knowledge to say for sure. As for teaching it to a class of children, well, so long as they understand that it's outside the usual system, and they can't use it in their day-to-day calculations, no harm is done. Perhaps it will excite a few that there are entire new sets of number-like systems out there. Learning about imaginary numbers (square root of -1) at a similar age stopped me going mad with boredom in maths classes and led me where I am today, with 2 maths degrees.

I agree with Evlis. I mean: a) In limitical calculation, terms like "0 / 0" or "a / 0" must not be replaced by new symbols, since they can be solved anyway b) Just giving it a name doesn't mean a thing. It still is not a number, since (I'll call the new symbol P): P = 0 / 0 = (0 + 0) / (0 + 0) = (0 / 0) + (0 / 0) = 2P that only makes sense if P = 0, which obviously is not fulfilled (in general). Of course, one should have a deeper glance on this work before judging it, but I don't even see where it should go...

Utter rubbish. They shouldn't be teaching this sort of thing in schools.

A quote of Richard Feynman seems appropriate: Now that doesn't mean anything. Suppose it's "Wakalixes." That's the general principle: "Wakalixes makes it go." There is no knowledge coming in. The child doesn't learn anything; it's just a word.

How is this even useful in anyway? does it even qualify as news - i know that not much happens in caversham but come on! A computer scientist should know better!

just inventig a new symbol is not worth mentioning. sorry. (if there are other theorems behind it, i missed them in this article)

Shadowkiller wrote: ___________________ So wait, let me see if I understand here. Nullity = 0/0. As the professor showed us, 0=1+(-1). So 0/0 = (1+(-1))/0 = (1/0)+(-1/0) = Infinity + Negative Infinity. As everyone knows, anything minus itself equals 0. So this means Nullity = 0. Do I win a prize? _____________________ Infinity + (-Infinity) are not the same number... u can not determine the subtraction's result.

Matt Milford
"Dr James Anderson, from the University of Reading's computer science department, says his new theorem solves an extremely important problem - the problem of nothing." Correct, haven't solved anything. Infact, you've defined it, these numbers by there nature are not defined on a conventional number line. "If it divides by zero and the computer stops working" Absolute BALDERDASH, this may cause a problem if the problem is not correctly handled by the program, which the majority of computer system implementations are capable of handling these days. By the looks of this article you make it look like this would be a valid symbol to use in an equation, which it clearly is not. You can check for an undefined answer from an equation but you cannot use this in algebra elsewhere. For goodness sake, do NOT teach this to year 10 pupils! Since when has this been part of the curriculum? More than the fact that I refuse to accept this, what practical application will this have to them?

Enigma in Norway
Divide by zero? What a load of codswallop! Division by zero never has, and never will be either a problem or a mystery. An autopilot cannot divide. It kan go bananas or switch off; but divide? Give me a break! Dr. Anderson would be better off using his energy on something worthwhile.

WTF!? pythogoras didn't worked?! I solve everything with A²+B²=C²! Even grades for wad reviewing.

what are you all on about? I'm the result when you divide by Zero!

David Heilmann
If you divide by zero, you have done something wrong beforehand. It may make sense so use 'NaN' (not a number) to catch the corresponding errors in a critical computer programme, but it does NOT make sense to cover up errors in mathematical reasoning by using just one more symbol, which would even make it necessary to alter other important mathematical rules (can you divide by that thing? If 1/NaN=2/NaN, ist then 1=2? In Short: unnecessary and destroying mathematical clarity.

He has only put new problem on top of the old one... nothing new about the that. He could just as easily defined that anything devided with zero is zero. Just as anything multiplide with zero is zero...

It´s all nonsense...
It´s all nonsense because instead of dividing ridiculous numbers people should better come together amd make different kind of stuff. Math is artifical (and boring), not real !

Phoebe Tunstall
This proposal is painfully stupid. He's applied a computing concept (the idea of having a symbol for "Not A Number" when a calculation cannot produce a sensible result) to general purpose arithmetic in a way which will confuse students. Actually it's worse than useless, because at least calculations which return the answer "NaN" can't be both equated together (2/0=NaN doesn't equal 4/0=NaN, as NaN isn't a number and as such no such comparison can be made) whereas Nullity = Nullity in Anderson's system. Whilst he may have been able to construct a consistent arithmetic system around Nullity, it's *not* the same arithmetic system employed in primary or secondary school maths (in the same way that non-Euclidean geometry is a completely different system to the Euclidean geometric system school pupils will be working with). The fact that he's not making clear just how radical the differences are between his number system and the commonly used one suggests he either has a very poor understanding of maths or he intends to mislead students into following his crankery for the sake of self-aggrandisement.

Arne G
Hm! Suppose we have one apple to divide between 3 persons in a classroom. Each will have a third of an apple. Let one person leave the classrom. There will be two persons left to divide the apple between them, a half apple each. Let one more person leave the classroom. The remaining ONE person get the whole (=1) apple. Let the last person leave the classroom, there will be no persons left in the classroom to see the apple left there, which means 1/0=0. Would that be a mystery or a "problem" at all? So, does a "nullity" really solve a "problem", which is not there?

Quote from the paper: "the transreal logarithm of a negative number is defined to be nullity. In both cases the logarithm can be extended to give complex solutions, though we do not describe the transcomplex numbers here." Since this contradicts nearly anything related with complex numbers, I would call it questionable to exclude the explanation which will certainly lead to a contradiction, e.g. Φ+Φ = ln(-1)+ln(-1) = ln((-1)*(-1)) = ln(1) = 0

Trevor Wood
This is very, very silly. I don't know what Dr Anderson got his PhD in, but it wont have been maths.

I just spent all morning working this out, my boss caught me and sacked me on the spot. Therefore 0/0=P45!

What??? I'm pretty sure there's no such number as 'nullity'. If there is a problem with autopilots and pacemakers dividing by 0, then they just need to be better programmed. Certainly dividing by 0 shouldn't be a problem for an autopilot if the programmer thought of this possibility.

So it's much easier to calculate with an infinite number instead of an undefinied...

Let nullity be defined Φ = 42 and the whole theory makes sense. 42 is the answer^^ You can also define Φ = apple or Φ = coconut Φ=0/0 simply means that Φ is the (or better: one) solution of the equation 0*Φ=0 which is solved by anything, not only numbers. An exception is infinity, because 0*∞ is still not defined. You could redefine it, though and give it a name, say ... infinitillity ϖ or something, or you could also use nullity for this, just as you like. You do not solve a problem by giving a name to the unknown solution. In fact, I do not see any Problem in 0/0 since you still have to watch out when dealing with 0 for example 1!=2 |*Φ Φ!=2Φ |*0 0!=2*0 ??????? Call it Φ or what you like, it may make sense but is no real use, because the main problem is that the zero element of a field does never have a multiplicative inverse, and this cannot be solved without touching the axioms of group theory.

Dr Tim Southern
Dividing anything zero gives either minus or plus infinity as an answer and has been this ever since I went to school (too many years ago now. It is very easy to demonstrate this answer and it does not need to go outside our current number range. It is therefore, an un-necessary complication to a system that works well as it is. The fact that computers return undefined as an answer to dividing anything by zero is a software problem not a mathematical problem that requires software writers to create the correct definition.

Steve King
0/0 = nullity - fine, I have no problem with that. However, to attempt to calculate 0^0 by converting it to 0^(1-1) is wrong, because 0^(-1) is undefined (infinite). Try 0^2 = 0^(4-2) and you will also get 0^2 = 0/0 = nullity, which is clearly wrong.

:) IF YOU JUST WANT TO SAY THAT 0/0 is nullity then kindly dont waste our time on the white board,because you started from something and landed back on the same thing. sorry for being harsh,but please sound more convincing next time and dont show it to children,so it to mathematicians.

Comenius University: first try to prove lim x->0 0/x and then I will be happy :-)

If I have a cake and two people, I divide the cake by 2, and they have half each. If there is only one person, they get the whole cake - I've divided by 1. But if there are no people, I don't divide by zero, I just don't cut the cake at all! Attempting to divide by zero is an error that can only happen in maths and computers, which is why your calculator gives you an error message.

That is so stupid... Is this a joke? What about NaN (or Inf) in floating point operations and non-classical calculus based on numbers inftly large (or small)? Does anyone else think not beeing able to divide by 0 is a problem?

Crazy Swede
Numbers outside the conventional numberline is not something novel. Consider that the squareroot of -1 = i The problem with Dr Andersson soultuin is that it is an axiom and thus by definition cannot be proven.

I just watched the first videos, and... honestly, I understand he has to go slow for the kids, but I still think its funny I go from 0^0 to 0/0 in one step (I was experimenting with this problem) where it took him like five. XD Now, to his credit, this is something like the imaginary numbers. You take something that can't be done (getting the square root of -1), say its not part of the real number line, and give it a name. Except, you know, you can actually DO SOMETHING with imaginary numbers. They are USEFUL.

Jamie Browning
This is a meaningless idea, which demonstrates lack of basic understanding in advanced mathematics. The bbc is irresponsible for reporting it as significant. Did the reporter try asking any mathematicians for perspective?

Steve Roles
This is utter nonsense. Forcing a computer to work around the fact that it can't divide by zero does not mean that it is now possible. In mathematics it is still NOT POSSIBLE to divide a number by zero.

Schau Un
Implemented in Java ages ago. Where is the news?

OK, great work. Now you have saved thousands of lives and are expecting the Nobelprice?

Today nullity is in the classrooms what next creationism?

John Titor
Very, very stupid... In 20 years, nobody will even remember this hack.

That's totally moronic. You can't just go "Oh look, let's create a new number defined as the answer to this centuries old problem!", then "Wooh! I solved a centuries old problem!" He's an attention seeking idiot.

The OS guy
0/0 is all values, at once. This proves it: 0.x = 0.y ( = 0) (0.x)/0 = y 0/0 = y/x You can substitute any numbers into x and y that you want, so this means that 0/0 is any number. You can substitute irrational numbers even...and how about imaginary numbers? You see, it can be any number you possibly want it to be.

I agree with all of you that claims that this is crap. I read some posts claiming that you shouldn't judge new ideas to soon and that the square root of -1 used to be troublesome. Only, this is nothing like it. As mentioned before, NaN (Not a Number) has been used for quite a long time with much the same results. Hoever, what is really troublesome is the media attention that this gets. You can't just report anything without checking with someone who knows what they are talking about. You should at least be able to mention that there are critics before publishing something like this. A sad event for the media community!

The mathematical aspect of this proposed proof is seriously flawed. Foremost, infinity does not equal 1/0. If you start off with a false hypothesis, everything that follows it can be proven true. That is a basic proof principal. That may explain why the subsequent parts of the proof appear to make sense to some people. However, the proof is flawed throughout its entirety. Initially, the false assumption aforementioned alone disqualifies the proof. Even if you can overlook this, when examining other aspects of the proof one would notice that the proof itself contains divisions by zero. One can't assume that since they are attempting to prove that division by zero can be correctly expressed, that they are allowed to divide by zero in their derivation of the proof. If divisions by zero were already allowed, this problem would not exist in the first place. The other major flaw results when examing the broad spectrum of the proof. Dr. Anderson begins the proof with 0^0=0^(1-1) and eventually ends up arriving at the conclusion that 0^0=0/0, or the greek letter phi as he denotes it in his proof. Any mathematician knows that 0^0=1, thus again we notice a flaw. I am certain that 0/0 does not equal 1. I appreciate ingenuity and innovative thought, however the integrity of mathematics must be upheld. This proof is not acceptable.

That's 30 min I'm not getting back...
I can hear the chorus in the background as I watch the video (a la Southpark)... James Anderson, dumb dumb dumb, dumb dumb dumb dumb dumb.... Isacc Newton, smart smart smart, smart smart smart smart smart...

Wrong... Just wrong, its the most idiotic idea I have ever heard. Its just a symbol for saying NULL or not on the number line because it is impossible. Crack heads... all of them. The chalk board says 0/0= nullity, which is false, any kid knows 2/2 = 1 3/3 = 1 etc, so 0/0 = 1 the problem is when you get 4/0 in which case, nullity is still impossible, because its just saying anything divided by 0 = nullity... thus nullity =1 thus wrong.

Wow. If 0/0=nullity, then what is nullity/nullity? Are we gonna make up another name for that? This solves nothing.

Mikael Palmgren

So if x/0=nullity, then x/(y-z) tends to nullity as y tends to z. "Tends to nullity"? If numbers were to "tend to" something that isn't a number, then mathematics wouldn't be of much use now, would it? The notion of the "conventional number line" extending to a point at which it is "outside the conventional number line" is ridiculous. There is a difference between solving a problem and rearranging it to make it somebody else's problem. So this is what you get when mathematics meets early 21st century attitudes to things, eh?

This is just an endless chain of incoherences. The worst thing, as a friend told me, is that this guy is introducing children to this kind of "stuff", to say the least. This is what happens when non-mathematical people try to get into mathematics, they hardly have an idea of what they're doing. Totally disrespectful.

... this is ummm interesting yet seems very unusable... but like it has been said.. maybe for future use. isnt the example of the apple being divided by 0 posted by Mahesh Sooriarachchi not 0/0? it would be 1/0 right? and HOW CAN YOU BREAK THAT WHICH IS NOT THERE? cant the answer just be no solution? haha. draw a picture, give it a name... voila YOUR A GENIUS. i guess this is kinda offensive but i really dont see a use. And also how can there be a point off of the number line? does that mean its not really a line but a graph?

Are you actually kidding me? He made a new symbol, he didn't change mathematics. "Oooh, look at me, this is a huge discovery: I can draw a new design!". This is actually sickening. Now every person is going to go around "changing mathematics" by saying that a picture of their face means some previously unknown number. Give me a break.

Ha! Math has already stated that any division by zero is undefined, he just took infinity and null and just made a fancy new word instead of using undefined. I'll wait until this computer science teacher gets peer reviewed by the mathematics dept and publish a paper before he goes out and runs to the media, and tell him that he should have learnt that in first year calculus course, and should stay out of the realm of mathematics.

0/0 = Nullity Okay so what ??

This is not a 1200 year old problem, nor is it newsworthy. All he did was assign a (meaningless) symbol to something that was equally meaningless, and make a few axioms for it. Sure maybe it's useful in computer science, but it's nothing that a programmer with a little math background couldn't do himself. Teaching this to 10th graders will only hurt them, because they're going to think that there's some actual numerical outcome to the arithmetic operation of dividing a number by zero, when it's really just a symbol that someone made up and tacked onto the extended reals. As my analysis professor said "definitions are neither true nor false, they're either useful or not useful". If Dr. Anderson's axioms have some kind of use then sure use them, but they're certainly not newsworthy, and they're certainly not a "solution to a 1200 year old problem that Newton and Pythagoras couldn't solve" as this article makes them out to be. Either this guy has a friend in BBC news, or they really need to do more homework on what they declare to be newsworthy. Is it so hard to google something and find out that the mathematical community thinks it's garbage?

Ajeet S. Arora
Hi, As we can understand that all mathematical function are the assumptions of one or more mathematician. as they said and did we are following that and if 1/0 could be infinity and -1/0 could be -infinity, so its an good idea he as proposed which is very simple that we should define 0/0 is something and that is nullity and which is quite logical even. So what no one can think of in these 1200 years, we should go for his theorems so that no calculator and computer should tell us on dividing on zero that function is not defined :) atleast we know now there is a result ... Better luck. Great Work

Robert Beaubien
The answer to divide by zero is infinity, not nullity.

Matt Green

Andy Josh
How is this new fangled "nullity" in any way different from the "NaN" (not a number) concept used in computer science for eons? It sounds the same.

BluE DicE
Nullity has always existed, it's just been known as 'undefined'. This guy is no genius, he's a fraud.

This is a joke, right?

D.S., Germany
I'm not quite sure if this person has found out something so "easy" and "basic" that no-one else seemed to care about or if he just "solved" a non-existing problem... Either way I'm really offended that he uses the kind of stupid name "nullity" - how would you translate that into other languages? For example German: "Nulligkeit"? Yes, it _could_ solve some bad-ass problems somehow... But I think it will be some 100-200 years that mathematicians will _really_ begin to use "nullity" ;)

a.c. cool
what about nullity/0 ? i dont think that the people with no mathematical background should comment unless youre asking a question. they just look stupid.

Anonymous high schooler
whats really so special able this? its like the square root of -1. its set outside of real numbers. can you set nullity into a graph? can you incorporate it into the unit circle. what have you changed? as far as i'm concerned you've just renamed "no solution." and now your students think your a genius. well, i'm going to rename you nullmind until i see your "theory" actually used for something. are computers going to be less confused with a definition of nothing? wouldn't nullity itself cause the computer to crash? i think you should check out both sides of the coin before you pay your students with it.

Proving beyond any doubt what so ever that 0=0. Bravo!

He stated that 1/0 equals infinity. In the third line from the bottom of his proof, he multiplies this infinity by 0/1. 0/1*infinity equals ZERO. Not zero over zero. Zero. Which is how many chicks Dr. Anderson is getting.

i did that once. a while back when Windows would boot up i started recieving an error message "cannot find file xxxxx" (divide by 0) Windows would then suspend at that error message. (ERR). so i solved the problem. i created a .txt file and named it whatever file Windows was looking for and dropped it into the System folder. (nullity) WOOT !!!1

Yesss, I think I grasp this concept. Wait! I just saw myself going out as I was coming in. Make it stop. Make it stop.

Chris Drost
He apparently demonstrates no knowledge of any advanced concepts related to his present situation. There's no mention of the fact that if f(x) and g(x) both go to 0 at some value x*, the limit of f(x)/g(x) near x* might be any complex number, or could even be infinite. We solved 0^0 a long time ago. It follows the form x^y, and has two different limits depending on whether you send x to zero first (because 0^y = 0 for all y, so the limit is 0) or if you send y to zero first (because x^0 = 1 for all x, so the limit is 1). We've further established that, in the most general case, the "best" limit for this scenario is 1, though technically the idea isn't completely coherent because the limit doesn't really exist in the 2d space. If x^y, for nonnegative real x and nonnegative real y, is actually giving us numbers off the real line, then we need to be worried, friends. Finally, you cannot define addition, multiplication, subtraction, and division in the standard way while still keeping nullity "off the real line." If basic arithmetic operations are allowed on nullity, it can be proven that nullity is any real number that you want it to be.

I just invented a problem to an "error" of science that neglects to answer the question of how our universe began. The answer is an intelligent designer. This designer lies outside our ability to perceive or observe it directly, and its essence cannot be isolated in a lab. By giving this concept the name "intelligent design," I've solved one of the Earth's oldest questions! Mr. Anderson's "theory" of "Nullity" is just about as useful. Those poor children.

this is the most pathetic attempt at proving something i have ever seen. the entire prrof relies on dividing by zero which is impossible and cannot be proven otherwise. this is a disgrace to even give this man any notoriety and BBC should get rid of this before anyone else wastes there time and reads about it.

1/0 does not "equal" infinity. -1/0 does not "equal" negative infinity. Stop treating infinity like it's suddenly become a quantifiable number that can be used in arithmetic. Sure, you can take the limit with either, using c/x as x-->0, but that still doesn't define what the result really IS at that point. All he's done is use rudimentary algebra to get 0^0 into another form, 0/0, to which he just recently assigned a bogus symbol. And now he's teaching it to students, as if it were real mathematics?

James Marino
I came up with a similar theory a few years ago during math class when i noticed that infinity and undefined on a two dimentional graph looked the same (they are the same according to me . . . they are just the opposite ends of infinity)

I have a Master's degree in Mathematics from a well-respected university in Missouri, USA, and I see what Dr. Anderson is doing here. The problem people are experiencing with this stems from them assuming Dr. Anderson is using the notion of "infinity" and "negative infinity" by the ideas utilized in calculus, where we can multiple these by any positive real number and it stays positive or negative infinity. Similarly, if we multiply them by a negative real number, we get the opposite. However, by defining 1/0 as infinity and -1/0 as negative inifinity, Dr. Anderson is distinguishing 1/0 as infinity, 2/0 as 2*infinity, and so on, where 2*infinity is NOT EQUAL TO infinity. Using Dr. Anderson's logic, inifinity plus negative infinity equals nullity. Thus, nullity does exist as an extended real number. It's much easier to see if you view infinity and negative infinity as being real numbers themselves, not the abstract concepts we learned in our basic calculus courses. You all bash Dr. Anderson and say he is trying to recieve credit for a pointless idea. He has just shown that there exists another extended real number!

Holy Googamook
Phwoar this guy roxors my world! this has Nullity uses, and Infinite amount of strangness.

The Drip
Sorry I am so late guys but I figured this out. Zero is not a number, it is a place holder for where a number would be. I can't distribute a number no times. This statd, I can not distribute nothing no times. Therefore any number dividing by nothing is equal to The Drip. This is a revolutionary number that stands for "anything you want" because the drip delivers.

I don't mean to be rude, because I like to try and discover things as well. I dont see a solution here, all I see is a made up number that replaces what was already there! Basically, zero was defined multiple times and then just made to equal some made up number...? On the subject of mechanical problems, they only exist because we tell them to. There is no magic behind a calculator erroring out...we gave it that error! So dividing a number by zero has just been given a name..nothing has been solved here.

Brett B
I love all the comments of people complaining that nullity is bull because it's not on the numberline. Progress comes from thinking outside the box people

Andrew Green
This is a disgrace to math, math isn't supposed to be easy and quite frankly find it insulting to find you mocking math greats by belittling them as inferior to school children's minds.

This is useful, but it's impossible to tell from the article. If you actually know math, read his articles on to understand the closure and definition of the operations on an extended number line.

I'm just going to teach my students that 0/0 = pineapples and then 0^0 = 0/0 = pineapples. Don't you see? This guy just gave 0/0 another NAME, not a solution.


Sir. Edward
nullity.. ti's crazy.

Joe Sipple
Obviously this guy knows nothing about computer science or mathematics. Nice try, and thank you for wasting my time BBC.

Per Alltrelén(
Zero or nonexistence can't exist. That nonexistence in the same time should exist is a greatest logical paradox of them all. Therefore should't we construct something which not exist in the reality.

Okay, let's kill nullity. I know a trick--we'll multiply by 0. 0^0 = 0*(0^-1) = (0/0)*(0^0) = (0/(0*0))*(0^1) = (0/0)*(0^1) =nullity*0 = nullity (see above) Huh? Okay, nullity cannot be killed. That's fine. Maybe I should just try to avoid it. Let's just try normal math. 2+2=4 2+2+0=4 2+2+0^1=4 2+2+0*(0^0)=4 2+2+nullity=4 ARGH!!! Well, thanks a lot, mister anderson, for disproving math. NOW what are computers supposed to do?

I don think this just works out! Now how do u define nullity and its subsequent arithmatic? Does proposing a new hypothetical "Nullity" solve this? Hmm I don't know! Kudos to every ones comments below!

If Dr Anderson was a solicitor (or an attorney in the USA), he would have asked what number we wanted 0/0 to be.

president of china
your argument is invalid

Congratulations! You just invented QNAN, +INF, and -INF! What the hell is this nullity word?

This idiot fails to recognize that anything divided by zero is infinity. We know this allready.

Richard Shetron
CDC computers have been working with 1/0 since the 60's. I don't remember the full details, but in addition to normal results from math they also have flags on every word that indicate if the result is x/0 or -x/0 so division by 0 does not produce an error.

While this is an interesting theory, I would like to see a paper or some form of actual theoretical work other than writing on a chalkboard. I am highly suspicious that he is indoctrinating his students with his theory rather than giving talks to the more mathematically developed.

B. Babic
Wait, so in other words nullity is undefined? He just renamed a well-known principle; is he clinically insane?

Jenna at EJSHS!!!
This guy is full of crap. He hasn't solved anything. What I thought was funny was that one of his first sentences, he was trying to define nullity and he said that it was a number that was off of the number line. WTF?!? Am I the only one that noticed that in one of his first sentences, he proves himself wrong. The number line is exactly what it means, all of the numbers. . . ever. . .INCLUDING INFINITY! Also, making up a 'problem' and making up an answer ISN'T SOLVING ANYTHING! Something else thats funny is that I'm only a freshmen in high school and in algebra I honors.

John Dillinger
Yes, but try getting a computer to understand "Nullity" :) It doesn't really have that much impact on real mathmatics at all.

How to define in base two? Because computer system works in binary level. If you can please explain how to define n base two or any other bases.

Anonymous Coward
I can't believe BBC would publish this crap. People say that complex numbers were criticized, and look at them now! The only difference is, complex numbers actually fit in with the postulates of arithmetic. Quite simply, we're looking at a number n such that n=0/0, meaning that any number c*n = n. c could be any number. Now, let's divide both sides by n. We'll be left with c=n/n. What's the only number where dividing by itself is any number? 0. Therefore, n=0. So, we're basically saying that nullity is zero, but, on the other hand, it could be any other number, too. Think about the logic behind division. What number times zero = zero? If you said any number, you're right. So, we're saying that nullity is both zero and every number at the same time. Anyway, it's easy to prove lots of things using Dr. Anderson's theory, but it's really just a lot of crap. Oh, by the way, anyone who wants to use the example of a pie being shared between zero friends, stop. If you have 1/0, nothing times 0 is 1, so you're wrong.

The problem with dividing by zero is that zero is not a number, its a concept- it has no value, no real existence outside the idea that if there's nothing of something than theres 0 amount of it. Likewise, infinity and negative infinity are concepts, not values. Thus what he's essentially doing is giving a concept notation (example:-1^(1/2)). He's not really doing anything that much different. The only real practical application would be to make it a value that calculators can understand (which, by the way, just gives programmers a giant headache trying to explain to a machine that what doesn't exist now does and has been given some value). I just don't see how useful it is as most computers are told to keep all zeros on top.

John VanDamme
Wow, they came up with something that was totally unneeded, since you already can divide by zero in higher math.

Great..... Another way to make math complex.... I knew there was a reason I hated it lol.

Wile E. Coyote
This is so simple! He states the meaning of nulity right up front in the discussion. Nulity lies off the number line, hence it is non-numeric and unmeasurable. if x = 0/0 x therefore is Nulity hence x = a fish Nulity is surealistic mathematics. Duh!

Agent Smith
"You have a problem with authority, Mr. Anderson. You believe you are special, that somehow the rules do not apply to you. Obviously, you are mistaken." -- from The Matrix

So, I've been ranting about all the holes in this proof for the past two hours to a few friends of mine, and it finally struck me why this was so frustrating- he's using circular logic to prove his "nullity"! He starts out telling us that "0/0 = nullity" and then ends with "0/0" saying "Oh, then this must be nullity, I was right!" (As a side note, I wonder if he shouted "Eureka!" when he figured this out?) According to the logic presented in this proof, if I cannot solve a problem, I can rename it. Problem solved. It's like Mitch Hedberg joked: "If you are lost in the woods, then build a house. 'I used to be lost, but now I live here. I have severely improved my predicament!'" This logic makes no sense. So because nullity can essentially mean anything, am I now allowed to use this to answer all my tests? "What'd you get for number eight?" "Nullity." "Oh, man. Me, too. We rock." It doesn't make sense! There never WAS a problem with 0/0... 0/0 = undefined. I think that this is basic algebra. I sincerely hope I am not the only one that is severely disappointed in Dr. Anderson for this fallacy.

Me thinks too much fish oil in the diet is to blame for this. Anything divided by zero is an indefinite number, that is the result is unknowable.

Brian Brian Bo Brian Bananna Fanna Fo finnan Me Mi
Damn you earthlings!!! You finally solved the enigma that has allowed for humanity's enslavement and kept mankind in perpetual ignorance. The light of truth has finally been revealed and means the undoing of your extraterrestrial masters' hold on your souls. For ever, the name, Dr. James Anderson will echo light-years throughout the universe, bringing enlightenment to all that exists and doom to all that stands in it's way-- kind of like when Rick Moranis went "plaid" in Spaceballs.

.ram? I want to laugh at this lunatic, but not badly enough to use Real Player. Ugh. I think I'm gonna be sick...

I am a math guy and a computer guy. There's not enough information here to make a judgment. I could see where it might be useful, but there's not enough there to be convinced. For instance, 1/0 = infinity in the sense of limit N as N approaches infinity? That's not necessarily true, depends on how you do 1/0. If you take 0 to be the limit of -1/n where n approaches infinity, his infinity is the opposite of mine. Also, is this essentially a computer science issue or a math issue? From a math point of view its really missing a lot that I don't think can be fixed, but from a CS point of view, with some definitions of 1/0 and -1/0 this might be useful. In otherwords, how would he propose to implement this in hardware?

To divide by zero it's too really .... egoistic!

Ben David
So essentially what I get out of this is that "nullity" is another way of writing d.n.e. Even if you were able to use l'Hopital's rule and not find an answer, the result would be undefined or "does not exist"

This should be in Wiki as definition of FUBAR. I'm not kidding...

Douglas Smith
I'd like to see how these school kids appreciate this nullity crap when they get to calculus, and have to start actually bothering to solve for the limit of 0/0, and not writing down "nullity". I mean, I guess I'll define infinity/infinity as Super Infinity or something while we're at it.

Øyvind Karlsen
I am sorry Dr Anderson but "nullity" is the same as zero. Look at this; 0*0=0. Dividing by 0 on both sides and you get 0=0/0; zero = "nullity". Or in words; 2 dolars to be divided equally between two persons, how much will each get? 2/2 = 1. 1 dolar to be divided between one person, how much will each get? 1/1 = 1. 0 dolar to be divided between zero persons, how much will each get? 0/0 = 0 (no one will get anything).

Seth Dix
You infuriate me, Dr. James Anderson. You are just as bad as your kids who will answer your questions to prove something in class with, "X is true just because it is." I guess your solution could be considered a "rhetorical answer," if such a thing exists. If not, let's define capital Phi = "rhetorical answer." Thanks for ruining the next generation. These kids will be responsible for the world when I reach the same point of senility that you clearly have found early on in life.

From scrolling down a few lines, I can tell that this is redundant. But really, the BBC is accepting this sophistry as an innovation? "Nullity" is only a means of symbolising the results of shoddy programming - any discerning mathematician would just apply l'Hopital's rule if he wanted to solve anything.

Dr Dodgy
Perhaps "Nullity" is the hidden meaning of life, cos i can't see it having any other use.

Joe Frisch
This has already been done, and in the right ways. Don't congratulate the guy for inventing nonsense, he's just going to confuse his kids.

Guy Tanzer
I'm not a mathematician. I fix and program and teach computers, and got into computer to get AWAY from higher math. This is probably flying high away in some ethereal, rarified height of mathematics us mere mortals never see and cannot appreciate. But it seems to me that yes, you can theoretically remove 0 from any given number an infinite number of times.... but if you're removing 0, are you actually doing anything at all? I can, in theory, write an infinite number of $0.00 checks from my account and send them to everyone on Earth.... but all that would happen is my bank would get very vexed with me. Maybe there will someday be something to do with this wondrous new discovery, just as i is used in electronics somewhere. But until then I think this is just a bag of wind.

Matthew McDonald
I once saw an equasion that, while individually all of the internal equasions were correct, the resulting answer stated that 1 = 0. The use of an informal falicy while "logically" working out the problem, was the cause of the flawed final statement. I believe this falls into that same trap. As stated many times by other people here, anyone can look at an unanswerable problem, add a magical constant, and make it work. It still does not answer the problem, it just makes the solver look good and waste the time of other, legitamate mathematicians who now must try to prove, or disprove the solution, which was never valid to begin with.

You made the universe explode

Of all the 1200 years gone by, think of the amount of people during that time that would have had the same concept of making a new number to solve it but havn't expressed so becuase it's such a cheap method.

This Guy is an Idiot
I have invented an imaginary creature. It is called the Great Lintughler of Blogenia. This creature does not exist, so instead of calling it The Great Lintughler of Blogenia, I'll just call it ₪. Now we can study the ₪ as if it were a real creature. "Nullity" is really just a shortened form of ERROR: DIVISION BY 0, and is no more helpful.

A concerned American
This Mr. Anderson should stop teaching kids garbage and go trisect an angle or something.

Adding a new number like this is a field extension of C, which is impossible.

What a quack. There's a reason this guy doesn't present this at a mathematics conference or publish the finding in a journal. Because anyone with limited mathematical knowledge can see through this. And it's so glaringly obvious that no one bothers explaining why it's wrong. BBC bought this from an attention-craving fool hook, line, and sinker. Maybe he's not so much a fool for having planned such a publicity stunt. Perhaps one can say that his mathematical career is ruined, but I doubt he had one to begin with.

what a joke... the bbc should be ashamed they published this...

His solution appears tautological. What is 0/0? Nullity. What is Nullity? 0/0. It has the feel of imaginary numbers, after all i is not really a 'solution' to the problem of the square root of -1, just a name for it. But since anything times nullity is nullity, there's no 'nullity' number line in the sense that there's an 'imaginary' number line. It looks like simply a name for the connundrum, and not an actual solution. Addmitedly, I suppose it would be an advantage to computer science simply to tell the computer the answer was some made up concept rather than throwing an exception.

I= hella smarter than Dr James Anderson
okay how is this on bbc news... he just decide a name for 0/0. but the truth is this is all wrong 0/0 is actually dumbassity

Nelson Selinger
Very interesting!

This guy basically made a new name for "undefined."

James Doberman
Its disappointing that a quality newspaper such as bbc would not realise what a poor quality article this is. They should really run this past an academic (or even average high school student) before publishing.

I have one major issue with what most of you are saying. 1/0 does NOT equal infinity, it is undefined. if you want to take the limit of 1/x as x approaches zero, then it APPROACHES infinity. You can't have anything that is explicitly equal to infinity. In mathematics, even infinity does not exactly equal itself. Infinity is a term used to define a generic, indescribably large number. It isn't meant to be used as an actual number.

So basically it took a Dr. to develop a problem school children can do, because they'll know that Nullity = 0/0. which means, 0=1+(-1). So 0/0 = (1+(-1))/0 = (1/0)+(-1/0) = Infinity + Negative Infinity. Which all together now = 0. So why not just stop at 0 and save those poor school children some pencil lead and a headache.

This is a horrible excuse for mathematics. So this guy took a concept that was already known (i.e. you can't divide by zero) and put a name on it. And called it a theory... Also, what the heck is up with the "If your pacemaker divides by zero"? Does he think all programmers are retarded?

John Spartan
So if -1/0 is negative infinity, then 0*(-infinity) = -1? If so then what does -2/0 equal? -2*infinity? So now you are able to multiply infinity by numbers? Well I guess you can, and then say that 2*infinity>1*infinity. But is it so possible to do ANYTHING to infinity since it's already infinite, a number with no exact value.

It looks all right, I still have trouble with it though, maybe im too used to the real number line. Is this just an "official" name and symbol for an indeterminate?

So basically it took a Dr. to develop a problem school children can do, because they'll know that Nullity = 0/0. which means, 0=1+(-1). So 0/0 = (1+(-1))/0 = (1/0)+(-1/0) = Infinity + Negative Infinity. Which all together now = 0. So why not just stop at 0 and save those poor school children some pencil lead and a headache.

This is just asinine. All this prof. has done is replace the word "Undefined" with "Nullity". We already had a way to express 0/0, we just didn't call it a solution, - because it's not - it's a representative term, and so is Nullity. I created a solution for 1/infinity: I called it "fhqwhgads", can I get a medal now?

Throws division by 0 Catches Nullity. A by-product of infinity, the computer continues to process forever, no longer remembering to keep the plane from crashing into the ocean. Its too busy doing infinite error handling. thanks a a lot. It feels like binary in base 3.

Kyle S.
I think he is just trying to be cool— and being really stupid in the process.

Wow. Terrible. I am ashamed for the field of mathematics.

so suddenly zero divided by zero is a nullty? would that help anything, i mean to say- would that do anything besides pick a name and symbol for "undefinded" zero divided by zero isnt going to start being one, it is just a name for the non named error that is "undefined", so would it actualy help out the math world at all?

Wow... this really is a complete waste of site space, though I guess BBC you succeeded in getting people to visit your site and ask "What were you thinking?"

Steve Baker
COmputers don't have to crash when they divide by zero - almost all of them do this as a courtesy to the programmer since no well-thought out 'real' thing every requires you to divide by zero - so it's almost always a bug - and you WANT the computer to crash so you can find the bug and fix it. If your pacemaker is dividing by a number that can every be zero then the program is already faulty for some reason. When you DO want to divide by zero, you can tell the computer's operating system not to crash the program. The IEEE standard for what the computer returns when you do this is called "Not-A-Number" or "NaN" for short. This is effectively the same as this guy's "Nullity". Mathematically, this guy is talking nonsense...and teaching it to kids before it's gotten widespread acceptance in the mathematical community is reckless stupidity.

This is completely ridiculous. This isn't math at all.

um, all he did was come up with a "new" number. Could have called it "X" and it'd be the same thing. And yes, nullity can be any number, so if you have 3*0=0 and you divide 0 from both sides you get 3=nullity. Now i can never be wrong on my math homework!

Carl Mel
Zero's zero's and more zero's! If I banged my head right now, I'd see zero's instead of stars!!!

This is absurd. As x approaches zero, then 1/x approaches infinity. Infinity is a concept, not a number. Undefined is also a concept, not a number. All this guy did was make up a name and a symbol instead of saying "undefined". Even if somehow, somewhere, what he is preaching is useful, what he has done is not at all original. This is just another example of idiots with PhD's going around confusing people and making the real scientists of the world look bad.

brian griffey
No, that's not mathematics. I'm graduating in may with a degree in mathematics and that proof doesn't mean anything. He is just defining his "nullity" to be 1/0 which isn't a number which means he hasn't solved anything.

whats the point of dividing by zero other then to fool and trap your enemies into a time paradox?

this is so my away message for the next 1/0 days. And the Quotes, OH my goodness the quotes! Those kids, I feel pity, oh so much pity for them.

You know, I had this idea ten years ago in high school. I told everyone involved with the math department and they all told me it was "stupid" and "useless" and "not mathematically relevant." Why can't my ideas be accepted and considered important just because I have a little piece of paper that says I spent 8 years in higher education?

YOU SUCK. There's no use for a creation of another idea to represent a divison by zero error. Any competent engineer or programmer would have coded a prevention system in place to PREVENT dividing by zero in an airplane or pacemaker. Your examples are nullified and your purpose is useless.

This man is a computer scientist, not a mathematician. I can't believe these kids are buying into to this garbage. I also can't believe that this man can believe that nobody else has ever thought up of giving a new damn name to an already existing concept, especially considering how NaN already exists and he is, supposedly, a Doctor of computer science. NaN works well, this is simply a stupid relabelling. Of course you've 'solved' it, you defined it that way in the first place! I dare him to send his into MIT, Cambridge or Clay, they'll shoot him down in seconds. BBC you should be ashamed to have featured this, slow day for news was it?

Amazing, Dr. Anderson has solved a problem that "hasn't been solved for twelve hundred (?) years," that "Computers simply cannot divide by zero," unless, you know, you use a *computer*. The BBC, amazing people who don't understand IEEE floating point arithmetic for 84 years and counting!

I'm ashamed that BBC would publish such bull. Seek a better mathematician's advice before lauding this crap.

Hah! I did this months ago, bored in Calculus class. Actually, I think I defined 1/0 to something. Whatever, point is that it's meaningless. Haha, at the time I defined the set of numbers including my new number for 1/0 as the "Ridiculous Numbers"...

Hanno Essen
I do not think that Dr Anderson's theory is entirely new. Yaroslav D. Sergeyev of the University of Calabria, Italy, has published similar stuff at conferences and has a patent application.

The only thing I see in that proof is that 0=1-1. And ... 0^0 should be 1 from what I remember ... then he proves that 0^0 = 0/0 = NULLITY? would that imply that NULLITY = 1? not very convincing :)

This isn't even a story. Mathematicians have understood this concept for years. He's giving another name to something that already exists, and teaching it to kids.

Daniel Palmer
Your peacemaker might crash if it does a divide by zero and one of the following properties are present; - The MCU running the code doesn't handle divide by zero or the logic to handle it doesn't work (this has happened in at least one MCU, don't know if it was ever used in a pacemaker). Remember a divide by zero would result in a infinite loop and alsorts of nasty things could happen :/ - The software running on the MCU is broken and isn't catching the divide by zero when the MCU flags it. I'd hope pacemaker designers test their code...

People aren't seeing the big picture
This does actually have practical applications in terms of computer science. Just because it isn't useful in everyday life for most of us doesn't mean that it has no value whatsoever; as mentioned earlier, we can decry "i" as useless, when it's very useful in specific settings. Congratulations to Dr. Anderson for reaching these conclusions; while I'm sure it must be disheartening to read all these comments dismissing his research, those of us who understand more about the problem actually see how useful this is. Keep up the good work!

Ken Stein
this is retarded, computers have had an error flag in the FPU for this for I dunno... maybe thirty years now? it's called NaN/Not A Number and does the job just fine. This "researcher" just came up with a dumbass name for something that already existed, he didn't invent anything.

When I did this in high school math class, it was rejected. I was told that it was not a valid method, was against the rules, et cetera. Why is it he gets to get away with this and not me?


I agree, division by zero is not a problem for computers, it's a feature. Programmers can override the error interrupt, place zero as an answer or handle it by other means.

Prof. Finkelstein
you can't define inf= 1/0. becasuse then inf*0=1 and zero multiplied with anything "kills" anything, i.e. inf*0=0. so: 1=0 ? answer: no!

Mark Wagner
Now that I've had a chance to look at this from a serious mathematical perspective, it makes no sense. Yes, he's managed to make dividing by zero give a sensible result. But in doing so, he's thrown away most of the properties that make traditional arithmetic so useful and easy to use. In abstract algebra terms, he's invented a set with two operations -- about the most primitive sort of mathematical system possible.

I have deviced to rename 316 to "Brian" - is that ok with everyone?

emo kid
Great, now not only do we have infinite depths of human sufferings, but now we had nullity depths of human suffering. Excuse me while I go cut myself.

Wathel Bloture-Herness
This is just more liberal propaganda that's trying to remove us farther away from God.

University of Toronto's computer science departmen
I feel bad for those pupils and for the fool that thought James Anderson should have "Dr." in front of his name. Do they not teach calculus in England? Any non-zero number divided by 0 is infinity. Let y = 1/x. As x approaches 0, y approaches infinity. Furthermore, the expression "0/0" is an "indeterminate form". That does not simply mean that it is undefined; rather, it means that if f(x) and g(x) both approach 0 as x approaches some number, then f(x)/g(x) could approach any finite number or infinity or negative infinity. It depends on which functions f and g are. See L'Hopital's rule. The reason simple calculators show an error is because infinity is too large to store in memory and also because they haven't programmed L'Hopital's rule into the calculator. A real computer scientist would know that this "problem" was already easy. Mr. James Anderson is just trying to make it complicated.

Wow... I guess even the BBC has an off day.

A number 0/0 is called an indeterminant form. So is (inf)*0, 1^inf, etc. Simply multiplying both sides by infinity (with the lofty assumption that infinity is a number), only results in another indeterminant form. Expanding products of 0, 1, and infinity again will only result in more indeterminants. All of the people that posted "proofs" did not necessarily do anything wrong, but the result is misinterpreted. As for all of the "proofs" that nullity is a fallacious idea take into account similar lofty assumptions. That is to say, Dr. Anderson did not say where "nullity" belongs. He only said it was off (what I assume to be) the real line. He, for some reason, didn't define any rules of combination for this number with other numbers, what its properties are, etc. From the video, it is not clear what you should be allowed to assume.

Ben Kershner
This is one of the dumbest things I've ever read. Where did this guy get his CS degree, ITT Tech? Wait, that would be a disservice to that reputable institution.

This is, sadly, the stupidest thing by far that I've ever seen 'reported' by the Beeb.

Dr. Alkhwaizmi typing from my wheelchair.
So this nullity thing, does it vibrate? Will it get rid of George Bush and TomKat, solve global warming, get me a Wii and establish World Peace? If so, I am all for it. No matter how impossible it sounds its just a matter of enough of us believing in it, by virtue of which the impossible comes into the realm of possible. I Believe.

haahaahaahaa... I am glad i did not go to Reading. Does the author have tenure ?

Dr Anderson has done little but assign a name to an already well understood concept. We call it 'undefined'. changing its name doesn't change the problem. This guy calls himself a computer scientist?

The concept doesn't seem much different than that of i, and it's considered useful in the math world. Unfortunately, he's made a big deal out of declaring that 0/0=0/0=nullity. Any number x^0=1=x/x; so obviously 0^0=0/0=1? This has an excessive amount of proof to show what would take a few moments of common sense. Why assign "nullity" to what can be proven to be 1? And division by zero we've said is infinity; and it's obvious x*0=0, so 0/0=x. This means 0/0 is any concievable number. It's good in theory, but what he did is unnessicary.

WOW. I wish i could make up numbers.

How can they allow someone to teach impressionable students a controversial topic without a peer review. I remember in 3rd grade, my (substitute) math teacher using '' (greater less than) in the opposite sense and until quite a few years after, I used to be confused while using them. What I am saying is that it is hard to 'unlearn' something so make sure you don't experiment while teaching basic concepts.

Donald Calloway
I'm a mathematician, and like Star Trek's Mr. Spock, I say, "fascinating!" I wonder what nullity to the nullity power would be? It's a number that is its own reciprocal, no? If so, then nullity squared is equal to 1, no? In fact, nullity to any power is equal to 1. But 1 is a number that is its own reciprocal as well, just not equal to one.

First Time Reader
Ok, I finally tracked down the paper where he outlines his arguments. Looks like the real numbers + nullity + some other infinities = the transreal numbers, and given the axioms of transreal arithmetic, you *can* divide by zero. All of the standard proofs that you can't (some are mentioned in this comment thread) are addressed in the paper, and he shows how they rely on assumptions in the axioms that are avoided in the axioms for transreal arithmetic and transreal analysis. Because transreal arithmetic can do everything standard real number arithmetic can do, yet can also handle corner cases that often come up in scientific computing, he's arguing that we move the floating-point numeric format for computers to conform with the transreal number axioms.

what a joke

Terje van der Meeren
So when you divide with the new number "nullity" which is outside the conventional number line, what do you get? Another number "infinity" which is also outside the number line?

Dr Neil Green
Im a mathamatics lecturer at Oxford University, i was emailed this page earlier today, and simply nothing has been solved. All has been proved is any number multiplied by zero = zero. As if 0/0= "nullity", "nullity" * 0 = 0, so numity is just representing any real or complex number. Altho nothing new has been proven i can see how it might be useful to 'lable' this singularity 0/0. But simply 0/0 is equal to any and every number all at the same time. In this case "nullity" is everything.

This guy is a *** idiot. He just gave a new name to something that was already known. He has not solved anything in terms of math or computer science. It's sad that it takes so little competence to have a degree in computer science.

Carboon Montley
Anyone can make up a number to solve a problem. That takes no skill at all. Like 2^x=-4; thats impossible. But if x={}, some number i pull out of my rectal cavity, it works.

Even if Dr Anderson's theory is not nonsense (I am not qualified to judge), its "explanation" on the BBC website certainly is.

He's simply renamed the term "undefined" and called it "nullity". That's hardly news. Maybe I can solve the problem of cancer by renaming it "consumption".

When he says he's 'solving a 1200 year old problem' I'm pretty sure he means it lightly. He's just defined nullity to be equal to 0/0 and showed a few different ways to represent 0/0. To a mathematician this is no more useful than saying x = 0/0. In fact it is no different. However, it seems like his students are interested in what he's teaching. I think I'd prefer to have a teacher tell my children to study real analysis when 0/0 comes up. Of course this is coming from someone who would be happy to help an inqusitive student work through Baby Rudin. Although, that may be a bit past the age and level of these students.

Who the heck was doing math 800 AD?

Blake L.
Uh.. What happens when you Divide Nullity by Nullity or any number (zero included) by Nullity? You have the same problem.

Gary Patella
Although I hold no degree in mathematics, I am fairly well-versed in the subject. After reviewing Dr. Anderson's demonstration, I felt that he has accomplished absolutely nothing. His so-called "theory" merely takes a quantity considered undefined and renames this quantity nullity. Dr. Anderson merely fiddles around with basic functions in his demonstration. He starts out with 0/0 and through unnecessary steps that can be applied to any variable, arrives back at the same number. The claim is that renaming this quantity "nullity" solves all of the problems that this value has previously encountered. But it does nothing of the sort! It is analagous to someone trying to make the square root of two rational by renaming it a/z. Taking this number, multiplying by 3, adding 5, then adding six, then subtracting eleven, and finally dividing by 3 will bring one back to the same quantity. But this does not prove, nor does it solve anything. In short, Dr. Anderson's "theory" should be rejected by the mathematical community.

So basically this "Doctor" Anderson has substituted the term "nullity" for what would normally just be an undefined outcome. This is not new, and he has come no closer to solving the "nan (not a number)" problem than Newton or Pythagoras or anyone else. This article is ridiculously misinformative and needs to be taken down.

stupid theory
what if you were to consider someithing divided by nullity 6/nullity=????? this whole theory is stupid

I have a B.S. in Mathematics, NOT a Phd but... This guy is a Doctor? Pacemakers and aeroplanes dividing by zero? Sure thing dude.

0/0 and x/0 are not limitations of math nor computer science. They are undefined. And that is not to say that we hope one day they will be defined... NO! They are undefined for VERY good reasons. Computers can already handle infinity, undefined, NaN , and i on an application by application basis. When you have x/0, there is no mathematical answer which will fit every situation. Sometimes you'd want to terminate, or re-do something, or try the next item, or ask for user intervention, or set the result to 0, or to 5 or to -999.999. It depends on the application. There is nothing elegant about giving up and using "nullity" which doesn't solve anything! In calculus 0/0 could 'effectively' be 5 or -77 or pi. It doesn't really EQUAL any of those but you know what I mean if you know calculus. Stopping at nullity is stupid. It presumes you are using math for math's sake. Asking 0/0 = ? is like asking "Where did you get your hat?" when you DON'T HAVE A HAT. It's not healthy to MAKE AN ANSWER FOR THE QUESTION, when we should recognize there is NO ANSWER. And there is NO NUMBER. Undefined.

David Cook
Again proof that reporters are dumb (and this CS teacher is even dumber). All he did is give NaN (Not a Number) a new name. FPU's have had the concept of NaN for years. Giving NaN a different name in no way makes it a number - it still can't be used in math because it is NOT A NUMBER! Geeze... this is basic computer science - take this guys degree away from him immediatly.

what the heck
So, since nullity = undefined, 0/0=nullity=undefined, and since 0^0=nullity, 0^0=undefined. Where has this brought us?

'NaN' and 'undefined' have existed on computers for years... How is this new?

Void of Space
I'm sorry but this is a solution that has been suggested by school kids since the dawn of time and been hammered out of them by the education system. Looks like the system missed one ;) As a fellow comp. scientist keeping an open mind, if he can get some mathemeticians to help him validate his theory then I'll give him credit...but only WHEN it's due. So nullity is the measure of how nothing, nothing is...sounds more like a rate of nothingness...perhaps irrate nothingness :P

Dennis The Tiger
The real trick is to divide the square root of any negative number by zero, and then survive the resulting black hole.

This story is an excellent Troll for artificial site content and comments. The proverbial storm in a teacup. Job well done.

'NaN' and 'undefined' have existed on computers for years... How is this new?

Mathew Guice
"Nullity" is an interesting tern to give to a concept that already has 3 terms (indeterminant form, undefined and NaN - Not a Number). Being able to give a term and symbol to a concept that has been around for hundreds of years is not genius. If Dr. James Anderson could show transforations through "Nullity" that would be genius, but it appears to be just as un-useable as the other terms in calculations. If an article like this is to be run, please do your homework as to what the real isse is which is being able to transorm calculations through a devide by zero problem (which still cannot be done).

John Summerson
Excellent work by Dr Anderson. Now all we need is a new name for the exact number that spans megative infinity to positive infinity. I shall call it 'Allity'. Bow before it's Inexpressable Truth. I also propose that the smallest positive number above 0 be called 'Smallity'.

Marko Seppänen
It seems like he has only renamed 'NaN' to 'nullity'. He has discovered a flat, round disc that already exists as the wheel (Not a Number) and given it a new name. Why invent the wheel over and over again?

Erik Naggum
There used to be a rule in academia that you publish OR perish. With the introduction of this brilliant piece of software engineering into mathematics, Dr. James Anderson may redefine that rule to publish AND perish.

Andy L.
Somebody may have made this point already, but I sorta glossed over after spending 15 minutes reading all the comments, LOL... The flaw I'm finding in Dr. Anderson's theory is that dividing by zero isn't bidirectional. That is to say, 6/3=2. I can reverse that with by multiplying 2*3 to get back to the original 6. How would you do this with an equation divided by zero? Unless I'm missing something, anything divided by zero would end up as nullity, so nullity times 0=infinity.

First Time Reader
Wow, what a sensationalist article! I'm really disappointed with the BBC for spreading misconceptions about the nature of mathematics, and promoting this flawed "theory" as a mathematical revolution, when it's plain to advanced high school students, and to any university-level mathematics or computer science student that: 1) Division by zero is *defined* to be meaningless because that's the only way to maintain useful properties of the arithmetic system, 2) that computers don't have a "problem" with division-by-zero, but are *designed* to flag it as an error for the exact reason it was defined meaningless in mathematics, and 3) making up a symbol for "0/0" is useless without creating a system of mathematical rules that is consistent, doesn't lead to contradictory statements, and is useful in application to mathematical theory or practical computations -- unfortunately, it has been *proven* time and time again that you cannot define division by zero without contradicting some other, more useful property. Anybody can make up any new system of mathematics by tweaking existing rules or creating a completely new set of rules. To be useful, it has to either prove something novel, or solve a practical problem that no existing system could solve. Tell me, what problem does "nullity" solve? (Hint: don't say division-by-zero in computers -- you can already check for divide-by-zero before it happens, and do *anything* in response. Replacing divide-by-zero with nullity just means you have a new value, which needs to be checked, and then do whatever you want. This doesn't open up *any* new possibilities in the design of computer programs.)

Dr Snuggles

umm... I'm not an expert at math, but I'm glad this guy never taught me. I made a formula for 0/0 once... had a fancy name and drew a picture that looked like my favorite cartoon character to represent the thing I just made up. Yep they laughed at me back then too... I guess you don't have to have a brain to work for BBC and make a story out of everything. I know a child that makes up words... maybe he can explain black holes to the bbc.

Ben Papworth
Good grief! Talk about missing the point! Dr Andersons theory is not about dividing a *number* by zero, but zero by zero. Dividing a number by zero will be infinite, but the same rule doesn't apply to zero.

Any idea when they'll teach this in the US? (if they aren't already)

Takeshi Yokomoto
This is complete and utter stupidity. All he has done is assign a name and symbol to the mathematical concept of 'undefined.' Division by zero is not possible, and cannot be made possible by the abstract conjuring of nonsensical variables which themselves have no meaning in any arithmetically cogent sense. I could rename the standard NaN (Not a Number) error message computer systems return when division by zero is attempted to any number of terms, pretend I'd answered some grand riddle and teach it to a classroom of young students who would accept it as fact without questioning me, but I would not be inventing a new number and I would not be helping the field- I'd be obfuscating mathematics and doing an absolute disservice to those students. Further, any software written after, oh 1985, will not crash just because of a division by zero error. Try it on a calculator. Does the software running the calculator crash? Of course not, it gives you an error message and carries on. This man is a fool, and I'd hold the BBC to a higher standard than to report on his foolishness. I am, for the purposes of full disclosure, a mathematics/compsci dual major at MIT.

Dr House
Call me, seriously, i'll solve this one out.

Divide by god, what would be the teacher's result.

That is amazing. I'm teaching my teacher tomorrow. :]

This is is just silly. As x approaches zero 1/x explodes to infinity but 1/x is NOT defined at 0. You know what that says? That the function 1/x has output of infinity. NO function has an output of infinity, we get very large. So does that say when we have an indeterminate limit of 0/0 that it is nullity instead of appling L'Hopital's? This is nonsense.

with respect to 'Ryans' 'number circle' number circle with 1 on top -1 below and 0 on the right, how about -0 on the left

To bad the reporter who covered this didn't recognize the real story, which is the scandal of having a crackpot like this putting nonsense into the heads of innocent children who deserve better. Very sad.

Using the math and definitions in his proof, you can also show that "nullity" equals "infinity" and "negative infinity".

I divided this news story by zero and got forty-two.

Lee-Jon Ball
This is nonsense. BBC should be ashamed. This isn't peer reviewed science. Its self-publicised drivel.

n/0=nullity therefore nullity*n=0 or nullity*0=n (for whatever stupid reason, how can infinity times 0 equal a number?) HAY GUYZ AM I DOIN IT RITE?

Anyone with even simple knowledge of calculus understands why this is complete non-sense. Zero divided by Zero can be any value include positive and negative infinity. It depends on the limit as you approach 0. If 0/0 is a fixed value it is very simple to create tons of inconsistencies in math as many people have already posted.

your pacemaker will die? the flight computer will crash? what the hell is he talking about? there has only been one recorded incident of computers crashing like that and it was down to crappy programing, not the the number itself. Even so, defining it as nullity doesn't solve anything

My name is Puschkin, I am a black and white Domestic Short Haired cat. As a cat I am not known for having any mathematical ability. But I must say that I worried when my owner almost died laughing when he saw this nonsense by Dr Anderson. Please Dr Anderson if you have any more of this rubbish please DON’T allow my owner to see it, he is still laughing and muttering “these silly University fools” as he wades through the complexity of a large NpfIT project.

Why does he start with 0^0? What's the reasoning for that?

I have discovered a truly remarkable proof which this text box is too small to contain.

Simply deciding to create a new value in computers means reprogramming every single bit of electronics that's out there-- and defining "nullity" in binary. Who's going to deal with all that, then? And what good is a nullity for a computer when it still technically means nothing?

Airplanes and pacemakers have safeguards against things like dividing by zero already. The computer checks each variable in the code to see if any of them are zero. If they are, the program inside it runs again to find the right results. In good programming a technology dividing by zero isn't a problem.

Dr. Ray Lashley (PhD Meteorology and Mathematics,
I couldn't give two hoots about this 'theory', but I'm really chuffed that so many people are talking about mathematics (I was pointed here from a forum I inhabit where mathematics isn't a subject that comes up regularly). I really hope this is what it's all about; enthusing School pupils and the public at large to think about maths. It isn't just dusty books in an old library, it's modern and cutting edge and absolutly vital to modern life.

I am funnier than you
Binary? That's easy. Each bit can be one of 0, 1 or Nullity. Yes you can fit 3 values into each bit, 9 bits into each byte. When buy a 1GB SD card, make sure it works with MP3 players that support Nullity. MP3 players that do not support such a number will blow your brains out when they divide by zero.

Basicaly this guy just showed that 0^0 = 0/0. But what does 0/0 mean? So far as I know, that is still a mystery

Just look at this: 5*0=0, right? So we divide both sides by zero, and we get: 5=0/0. So nullity equals five, simple as that.

Brain on red
2+2=5_for sure!!!!

Angry Reader
Anyone in their right mind would have realized that this man is in deep mental trouble. By publishing his childish nonsense the BBC actively harms the reputation of Reading University. This is not funny!

Pr. Fredrik Åkerlund
Nullity or what it was called E R,C,N,Z, huh, where???

Taoist? "Tao can be be talked about, but not the Eternal Tao. Names can be named, but not the Eternal Name. As the origin of heaven-and-earth, it is nameless: As "the Mother" of all things, it is nameable. So, as ever hidden, we should look at its inner essence: As always manifest, we should look at its outer aspects. These two flow from the same source, though differently named; And both are called mysteries. The Mystery of mysteries is the Door of all essence." -Lao Tzu translated by John C.H. Wu

Josh Patton
This Ryan guy just a little above has the right idea about the number line being a circle with +1 opposite of negative 1, and zero opposite of an undefined number between + and minus infinity. Makes a whole lot more sense if you look at the calculus and the real application to a problem. Being an engineering student I cant see how nullity would make anything easier when it comes to solving an actual problem. So you get a vertical asymptote because you divide a number by what is a very small number tending towards zero as the y axis goes to infinity. What is the real world meaning? What does that asymptote mean for your system in terms of real behavior? This Anderson theory is not solving anything meaningful by just assigning an undefined value a name or symbol. Which by the way is the capital letter Phi from the greek alphabet. Redefining some quantity (undefined or not)and plugging it in to an equation does not make you a genius. But hey what do I know, I'm just a 4th year engineering student, no PHD here. Back to studying finals now :P

Connie Buller
So Gauss' proof that the complex number system is complete is not enough? It is fine to define nullity, but then it must be specified that nullity times 0 equals 12 one time: 12/0=null; equals 14 another time: 14/0 = null, and so forth. Possibly he has re-defined division to be something other than the inverse of multiplication.

I'm only a Calculus student, but I don't buy his definitions. If Infinity = 1/0 Then Infinity * 0 = 1 This is a problem. Why? 1 * 0 = 0 Yes? Let's try this then. Ininity * 0 * 0 = ? We can replace Infinity * 0 with one as shown above. 1 * 0 = 0 Which means Infinity * 0^2 = 0 But the problem with this is 0^2 = 0! Therefore you should be able to substitute 0 for zero squared. Therefore Infinity * 0 = 0 as well. Which means 1 = 0 because Infinity * 0 = 1 and Infinity *0 = 0. That's kind of a contradiction.

This lot should stop wasting time and just learn the cirriculum of the course. I think it is impossible as well, but we shall see...

My view of the problem. 1 Idiot/1 Idiot=Nullity Idiot

I don't see how this is any worse than 0!=1. And mathematics calls it a convention.

I don't see how this is any worse than 0!=1. And mathematics calls it a convention.

Firstly, if he's confused by schoolchildren [read the caption for the last picture again] what is he doing there? Secondly, he's a computer scientist, not a mathematician. This is computer stuff, not maths. Thirdly, it seems pointless at the moment. If it is going to be as accepted as i, [as he's probably hoping] is there anything you can do with it? Does nullility+nullility = 2nullility? Or just nullility? Fourthly, I don't see how he's solved anything, like the person who first came up with i hadn't solved the square root of minus one, he'd just defined it. Nullility is just defining 0/0. Fifthly, this is just an excuse to throw another Greek letter into the mix. Sixthly, I do hope they know that if they put that on their GCSE they won't get anything for it. I hope nobody does worse than they could have done because of this. Yours, first-year-maths-student-who-never-considered-Reading.

The problem is not the outcome of the zero division but how the computer/device has arrived to this operation to begin with. If the computer is dividing by zero than an error must have already occurred a long time ago. Plus, practically, the value isn't as important as how this value will be used to take some action. If I am using the outcome of the operation to adjust the pacemaker's frequency, how is nullity going to be any useful? I am sorry, but I think it's a whole load of crap.

your mother
i believe i speak for all mathematicians out there when i say *ha - ha* O_° this is more ridiculous than that one guy who claims he reinvented relativity saying speed of light is actually zero. i can only pray that this nullity thing IS a joke, unlike the above. peace

that would mean Everything equals nullity. Because their are infinetly many cases of f(x)/g(x) where x goes to some number it goes to 0/0 and could be anything depending on the limit. Any computer correct program knows how to take limits. This guy just poisoned the minds of several students.

that would mean Everything equals nullity. Because their are infinetly many cases of f(x)/g(x) where x goes to some number it goes to 0/0 and could be anything depending on the limit. Any computer correct program knows how to take limits. This guy just poisoned the minds of several students.

Finally, we can divide a number by the number of friends this guy has

Wouldn't nothing divided by nothing equal everything? Since nothing times nothing is nothing. Then nothing divided by nothing would be nothing. You can't divide a number by zero because nothing can't make something.

Divide by 0, I want what hes smokin.

If "infinity" stands for the fact that there ALWAYS exists a number greater than Y, then X in Y=1/X will NEVER reach 0, because X can ALWAYS be decreased (if it couldn't be, infinity wouldn't exist). Ergo, what you're trying to name "nullity" here has never existed and will NEVER exist. Calling "it" (in quotation marks because an "it" would exist) a "number" makes as much sense as non-sense (let's call it "non-sensity").

Perhaps this amazing solution will allow Kevin Warwick to make his robots actually work!

CAUTION Schoolchildren!!!
Dr James Anderson, speack about your theorem in front of mathematicians! CAUTION Schoolchildren

that would mean Everything equals nullity. Because their are infinetly many cases of f(x)/g(x) where x goes to some number it goes to 0/0 and could be anything depending on the limit. Any computer correct program knows how to take limits. This guy just poisoned the minds of several students.

Here are some facts. You can express infinity and -infinity if your computer uses IEEE floating point arithmatic. Most modern computers do. 1/0 is infinity, -1/0 is -infinity. Both are well defined. Infinity is not the largest number, Infinity*infinity is larger than infinity. Infinity*infinity*infinity is larger than infinity*infinity, ... In IEEE floating point arithmatic, Nan (not a number) is used when the answer is undefined (e.g. 0/0, Inf*0, ...). IEEE arithmatic has both +Nan and -Nan. For example: +0.0/+0.0 --> +Nan but -0.0/+0.0 --> -Nan. 0/0 has an answer we just don't generally know what it is. Sir Isaac Newton's showed us a method of obtaining the answer if we know how the two quantities involved in the division approached zero.

Mr Sven Persson
When i divide by zero on my Mac the calculator says, in swedish, "oändligheten" which means infinity, endlessness. Very beautiful.

Chris H
Since this is not a problem in mathematics, my guess would be that the journalist failed to understand what they're doing at Reading. They are probably just using a special value to represent the result of dividing by zero in a computer operation and this is probably a minor variation on the existing special value NaN (Not a Number) used in floating point operations.

the Eastern religions got this years ago... its called ZEN

In reply to PK, nulity is probably any number you want it to equal. I was taught Nuffield Physics and the answer to any problem was some "magical" or should I say "natural" co-efficent ie PI = 3.?????

It makes sense, but all he's doing is just calling one thing (an error), something else (nullity), which is not at all useful in normal mathematics (nullity is not a number, like pi or i, it's every number simultaneously).

I get it, nothing else for the news to report on so they hire some guy to make up something lame like this to fill in for important stuff. Lol.

Doktor Zero
According to my calculators 1/1 is "Error" or "Ma Error". Is that the same thing as that strange sign? Sounds easier to use Latin letters... Why didn't he write "Ma Error"?

Jason Kerwin
This man is painfully mistaken. Has he ever studied mathematics? I am appalled that he's teaching his kids something a) incorrect and b) that he made up.

Computers are currently able to divide by zero, and the result is NaN. (Not a Number) No crashes, no pacemaker deaths. The traditional divide-by-zero problem is with integers only, and is there for a reason. It speeds up processing if the CPU doesn't have to check for that possibility and deal with it. While the nullity may have some use in mathematics (or it may not, for all I know) I doubt we'll ever see it implemented in hardware.

Oscar Jenkins, UCDHSC
In any field, division by x means multiplication by the multiplicative inverse of x. So if division by 0 is defined, then there exists some number y such that 0 times y = 1. No such number exists in a field. It follows that this new structure is not a field, and therefore, new axioms for division must be defined for this system to make sense and for the notational manipulations to be well-defined. To wrap it up, you cannot justify the use of field axioms if you are not in a field.

By the way ...
1/0 is not infinity; it is undefined. Also, -1/0 is not negative infinity; it is undefined, as well. Any professor of mathematics with a shread of intelligence will tell you that. Furthermore, 0/0 is indeterminate. Do you know what indeterminate means? Apparently not. It means it cannot be determined. There is a great difference between undefined and indeterminate. Mr. Anderson, you should be ashamed of yourself for teaching your flawed "theories" to schoolchildren. I hope the university fires you, and your degree is recinded. Furthermore, this so-called discovery is essentially equivalent to an error trap; something already known to computers and their predecessors, Turing machines.

I guess this is another 'number' for students to work with, such as 'i' (the square root of -1). It will be interesting to see what they manage to solve with it.

Alex J.
So, they just invented a number and are working to convince us that x/0 is that new number? We need an infomercial for this... Have you ever tried to divide by zero and got an error? Have one or both of your grandparents died because of this? We can't bring them back to life but... NOW YOU CAN DIVIDE BY ZERO !!! Presenting NULLITY !!! And if you call in the next 10 minutes, we might bring back one of your grandparents (we choose which one). What are you waiting for, call now, now, NOW !!!


So basically ...
... your so-called "nullity" lies outside the real and imaginary number lines. If it's not real or imaginary, then what is? (other than totally flawed)

"Infinity + Negative Infinity. As everyone knows, anything minus itself equals 0" Not anything. Infinity is undefined. What if the positive infinity had greater magnitude? The problem with infinity minus infinity is that it is an indeterminate form. The problem with many of these equations is that they are supposed to equal infinity, when really they are approaching it. If I were the parent of one of these kids, I would sue the prof for spreading such bullcrap. The issue of division by zero, as well as infinity minus infinity is well solved in Calculus using L'hopitals rule. And as far as pacemakers and airplanes crashing, yeah, it has happened, but I think programmers have learned to catch the errors now.

Peter Freeman
It will very likely have the same impact as the invention of zero (Arabia), a concept that Roman mathematicians did not have and limited (along with their difficult numbering system) their mathematical progression. Once the concept of zero in the number system had been symbolized and rules around it were discovered, mathematics went a long way forward.

i think this is a big step for the mathamatics history. many problem happens all the time when diveded withe ziro, many new technologies for example. well done Dr anderson. Erik Norway

Haahhaah! The worst thing is I think the guy is serious!! WOW, Reading University seems like a really good uni!!!!!

How can we understand his therom if we aren't even told what it is and how to perform it? All this guy is even saying is that he made up a number. He essentially pulls math out of nothing! Besides he doesn't have a proof for it yet, therefore making uncertian if all results reached are correct. Even if it does exist and he can do it, and if the "nullity" sits ouside the numberline Computers couldn'tcomprhend it, since they cannot even deal with Imaginary numbers.

Ian Langmore
Are you stupid? Looking over his "axioms" on his website (I can't believe I did this...) you can see that his nullity nonsense is just the extended real line with this added number that comes about whenever you previously tried to do something that would produce an error. His axioms show that once you produce a nullity (i.e. error result) there is no way to get rid of it (you can't divide it out or subtract it and make it go away). So all his "results" could be interpreted as: "lets work with the extended reals, then if we get an error our answer is an error we stop" There would be no reason to continue working since from then on your answer is always nullity.

His theory isn't even a theory. A theory should provide a solution to the problem, rather than introduce more problems. It's just as bad as those conspiracy theories circulating on the internet.

A lot of people here have been making the statement that 1 / 0 = infinity. This is simply not true. It is undefined. Why? because the answer (infinity) does not meet the requirement of division. Normally if you take the result of a division, the quotient, and then multiply it by the denominator (0 in this case) you get the numerator (1 in this case). 0 times infinity is not 1. In some special circumstances, infinity is a useful number for 1/0, but not all, and that's why most CPU's have a way to tell the processor to either produce a divide-by-zero exception or to set the result to IEEE-754 infinity.

Rodrigo de Godoy Domingues
Yes, the concept is quite simple, but more mathematical analysis has to be made in order to proof the validity of his theory. By the way, it was a clever idea. Now, hands on... :1)

I guess stupid has no lower limit.

So...this guy gives a name to something that already has a name, and he gets a news story? Hey, BBC, can I rename you to UBC and get a news story too? I mean, it's only fair because you did it for this guy.

Andrew Punch
The crux of the problem with this theory is that it is likely that this new representation will have exactly the same restrictions as division by zero. The problem with division by zero is that the result is "undefined". Which means that you can't use it in subsequent calculations. He would need to come up with a rigorous proof, similar to the proofs that are involved in complex numbers. And since this is a *maths* problem not a *computer* problem I am very suspicious that this theory comes from a *computer science* researcher.

Jeremy Petzold
Congratulations. I had this Idea during my number Theory for my undergrad but never bothered exploring it beyond writing a short unpublished paper on the conjecture.

Kevin Kadium
Why would you want to devide by zero in the 1st place. Think of it logically, Yes it its a math equation, and yes its nice to think of a way to solve it. But honestly everyone is right. All your doing is makeing a error message turn into nullity. Thats not solveing the problem thats, just replaceing an error message. as LJL said, "doesn't a number lying OFF the number line violate the axiom of Completeness?" How can you be teaching this? It's Rediculous.

"Nullity" is newspeak for "undefined"

what problem of dividing by 0? I fail to see how this is any better than taking the limit of a function as a variable in the denomenator approaches 0, after all 0 is much like infinity, it is not really a number - even if it is able to be used as one - but a concept of none. After all having 0 apples is really not having any, rather than saying the number of apples I have is 0. While common language would allow for such a statement the idea behind it is incomplete. To call 0 a number is not nearly as incorrect as calling infinity a number, but it certainly is not as accurate as saying 1. of course that actually equals 0.999999999... :D

He really hasn't solved anything. Division is always reversed by multiplication. For instance, 4 divided by 2 equals 2. And 2 times 2 equals 4. However, If you divide 4 by 0 and the answer is "nullity", then that means you could multiply "nullity" times zero and get 4. Impossible.

Assumptions for the win
so what he just proved is if we have an unsolvable problem, all we have to do is change the name of something and it's solved?

Dave Korn
Dr. Anderson is nothing but a self-publicist who has made up a new name for something that already exists and is now pretending to have invented something new. He has done absolutely nothing of the sort and he has invented nothing. Computers have been able to represent one divided by zero for years; they use the term 'NaN' (stands for Not A Number) to describe it. Saying that 1/0 "sits outside the conventional number line", as he puts it, is exactly the same as saying that it is not a number. This story should never have been published. Journalists are meant to check facts, not just accept whatever they are told by a self-interested third party and publish it without question. Also, someone should tell those poor kids that they aren't the first at anything and their teacher has been deliberately misleading them. Come to think of it, he should probably be struck off for lying to his pupils for the sake of his own personal advantage.

Um, no. You can't just make up arbitrary rules when it comes to math. Did he write a proof?

Mileva Marick
So a new sybol solved it all?Interesting...

There are a few *simple* falsities he writes on his white board. (1) 1 divided be zero is not infinity you cannot say 1/0 = infinity. The definition of division is a/b = c if and only if there exists a unique number c such that a = b*c. So by saying 1/0 = infinity, he is claiming that 0*infinity=1, REALLY??!! (2)In his proof when he gets down to (1/0)(0/1) = "nullity" he's forgetting that 1/0 = 1 and according to him, 1/0 = infinity, then that line of his proof reads as 1*infinity = nullity. Silly me, I thought that 1*infinity = infinity!

Bill Merrill
This doesn't seem to be about dividing any number by zero except for the number zero. Therefore, it doesn't solve anything, unless I'm missing something here. If I begin the problem by asking about the value of 2 raised to zero, following the methods in the video I end up with it equaling 2/2, or 1. Thus, any number raised to the zero power is one, except zero, which is nullity. Not sure where this gets us....

J. Pehkonen
You guys are defining your own mathematical rules for this number, and then disproving his theory by using your own made-up-rules. Remember that in imaginary numbers i^2 = -1. Perhaps nullity also has its own mathematical rules? The same goes with INF/INF not equaling 1.

I think nullity is the last number in pi!

Scott Perry
If you've ever done any programming, you'll know this is old news. Dividing by 0 is something that programs can be written to catch. If they don't, the computer doesnt just die -- the Operating System kills the process that tried to divide by 0. It's not terribly hard to check your denominators.

I have a problem, I don't know the answer. I think I will just make one up! Hopefully no one will notice if I do lots of workings out to confuse everyone. The only thing this guy is teaching is how to be creative. Some thing maths is not. Obviously he is not a real mathematician!

Luke Whiting
Any programmer worth his salt wouldn't allow a divide by zero to occour in the first place! It's never been real problem in modern programming. I think this is all a bit silly. "I know. Lets fix a problem by adding a new number to the world".

When computers divide by zero, they continue working. x/0 = DivideByZeroException. It's called error handling and unless you are one of those idiots writing } catch (DivideByZeroException dbze) { // DO_NOTHING } you will never have a problem

David Turner
To all you people who talk about diving cakes between people... Divinding isn't about how much is left once you've handed out the pieces of cake... Trying to apply division to cake, you don't say "How much is left after giving this to X people", you say "How much does each person get"... So the division-by-zero problem in cake terms would be "If you divide this cake between no people, how much cake does each person get". At first Nullity sounded like a good idea, but it's not really a solution, just renaming the problem, as others have stated.

I hope someone is going to re-educate these poor children afterwards. The BBC should be ashamed of themselves for publishing this.

Baron von Mannsechs
Good job Ranjit--confuse Science vs. Engineering.

Jake Haseman
...Infinity anybody?

Question Dr. Anderson?
"...It is just an arithmetical fact that 1/0 is the biggest number there is.... " --- If 1/0 (infinity) is the biggest number there is... then is .5/0 or 2/0 twice and half as large? --- Does a number half of infinity divided by infinity prove 2=1? --- Why do existing rules about treating non-numbers outside the number line not apply here?

My pacemaker divided by zero and nullity happened.

I hate it when my bike divides by zero and the brakes stop working.

John Good
How is the definition of Nullity different from that of Infinity? Or for that matter "Undefined", which some calculators will spit out if you try it. I've got a better name for it: BS

This is some kind of joke, right?

Matze M.
I wonder how long it takes until somebody tells them that at the very position where they placed this "nullity" is already (0 - 1*i). But until then, it's quite worth a laugh. Thanks, man. Made this day a funny one.

Will this cause Bill Maher to hate and deride practicing Christians, and Catholics in particular, any less?

THis is compleetly wrong. a^0=1 Therefore Nullity = 1

ok.. this kinda makes sense, but what about infinty divided by infinity? Is that 1? I tried to use my texas instruments calucator but it just shows an error...

Step 1. Create solution 2. Create problem 3. PROFIT!

The New Math
turns out nullity is also the last decimal digit in pi.

Desperately Seeking Sense
I get it. I don't know if it's terribly useful, but I get it. If zero is like a void, then nullity is like an endless table with empty cells. However, once you apply a value to it, it becomes infinite by any means, therefore becoming infinity. (unless you can have: [infinity] * 2 ) Maybe that's for Dr. Anderson to figure out next year. I love imaginary numbers; they're like imaginary friends you can share with really smart people.

Daniel Asimov
I am a mathematician. Mathematicians have been gracefully dealing with division by 0 for millennia. It shows the massive incompetence of the BBC News Division that it would not have occurred to them to check with a mathematician before turning this report into a news broadcast.

Ramesh Arakoni
Why do you waste your time (and mine) publishing such rubbish.. btw.. what we like to call NaN (not a number) has been given a new name and oh.. nullity/nullity= insanity :)

Leo C
It's nonsense my dear dr. Anderson. You've solved nothing with this theory.

Way to go, you renamed the error message. You still don't understand the nature of infinity, or as you have now decided to call it, "nullity." From what I've read, nullity encompases positive infinity through zero through negative infinity, which could also be refered to as INFINITY. You just called it by a different name, you didn't solve anything.

CS grad student
Holy cow! From what school and department did this guy get his PhD? Such bravado and immodesty - Unbelievable. It makes me respect real mathematicians even more.

I believe that the problem is still not solved, because Dr Anderson considers that zero over zero is equal with zero (0/0=0) and he replaced zero with 0/0 in beginning. The fact is that 0/0 is unknown, and it doesn’t have any specified answer, zero is just one answer of many answers to this devision (0/0), this is in contradiction with a simple division like 18/2=9, because in ordinary divisions you get a specified answer. The problem with “nothing” will never solve because “nothing” is an agreement.

Why did you name undefined?

Richard C. Mongler
I divided by zero and the universe imploded.

stupiditus stupidensis
Just plain stupid. I wonder where he got his diploma...

Leo C
It's nonsense my dear dr. Anderson. You've solved nothing with this theory.

Sorry guys, this thread fails. There already is a symbol for 0/0. It's "O SHI-"

Ian Bennett
Null is hardly a new concept. Databases has been handling the concept for years; a field which has had no value entered, not even a zero-length string, is 'null'. A null field has no length, not even zero. It's good that children are being exposed to the concept.

So you can solve a math problem by making up a symbol? Wow.

I love the way all of these 'non-mathematicians' use arguments like "If I divide a pizza among 0 people I haven't done anything to the pizza so I have one pizza." To show why it's wrong, you need to realize that the question is wrong. It should be more like this: If I divide a pizza amongst 5 people, how much did each person get? A fifth of a pizza. If I divide a pizza amongst one person, how much did that get? One pizza. And then you can see logically why you can't divide things by zero normally. If I have one pizza and divide it amongst 0 people, how much did each person get? It can't be zero pizza, that would imply there were people to get one pizza. It can't be one pizza either, because nobody is getting a whole pizza. What Dr Anderson says is that if I divide one pizza amongst zero people, those zero people are getting infinite pizzas! It's laughable.

I think this could have good use as a backup if electronics or computer accidentally divide by 0, but other than that I don't see any real use.

ewwww, that's disgusting. Seriously, you really shouldn't teach students anything that doesn't have a solid scientific background. It'd be like ... teaching creationism.

JImmy Ruska
Division is a function intended to break an input equally into a set number of pieces. Without giving a valid number of pieces you want your input to be equally divided into, you are invalidating the purpose of the function known as division. Replacing an unworkable or unknown value temporarily with a letter is not something novel. There's no need to super impose an I over the 0 to be fancy. I can't see how this is a novel idea, and I can bet any efforts on algebraic simplification has been well exhausted.

don't really need to know
dude.. he just took out a 1200 equation by making 0 devide by 1 b4 he applied powers? the number 1 rocks lol btw thx mate u just took down the whole of calculus! btw anynumber devided by 0 is either a: not possible, b 1, c 0, d the number itself, e infinity- please make this a vote bbc!

Has anybody an insight into what rank the zahlenkoerper of Dr. Adersons's findings has?

Erik Schaefer, Madison, WI
I hope this gets world-wide acceptance because I want to be the first person to have the moniker of the only man in Wisconsin who has had sex "nullity" times.

omg nothing is nothing???? MIND = BLOWN

A proof of the mathematical inconsistency of this construction. First we'll take what he has written about the real number line. Namely, the reals are the rational and irrational numbers. Then we add in +/- infinity to get the extended real numbers. He then writes infinity to be 1/0. This is all we need to show that there is a mathematical inconsistency which we do presently. Now, since infinity now can be expressed as a rational, it is an element of the rationals. Since the rationals are a subset of the reals, infinity is an element of the real number system and thus is an element of the extended real number system. Thus, we have a contradiction because infinity is defined to be both internal and external to the real number system. QED

cannot divide by zero world will explode they are brainwashing kids to blow up the world by doing 'math'

The end of the world is here.

Jordan Lund
Creating a new imaginary number doesn't solve the problem, all it does is assign the problem an imaginary status.

how embarrasing
What can we in turn learn from all of this? Avoid embarrasing yourself on an international scale by taking 10 minutes to go down the hall and check with the math department to make sure your ideas arnt stupid. He could have at least put his ideas up to peer review before forcing it on his students and parading it around as mathmatical fact.

Dr Sanford Grace
This man is a blithering idiot!

Ned Peters
Tell me this is satire. Please, please tell me this is satire. If it isn't, then whoever wrote this article should be fired and and not allowed back into the press until he sucesfully completes a high school mathematics course. Or a middle school one, for that matter.

Magnus Maximus
Humankind introduced zero in the 15th century, which was considered decisive step in sciense. Now, why does humankind dismiss zero? Just to reinvent it in 1200 years??

This nullity idea is meaningless. He hasn't shown why it's useful. Also, it has been agreed that x/0 = +infinity, where x is any number between -infinity and +infinity, so his proof is pathetic and hasn't solved anything. In fact, he has just re-iterated something that has been known for a long time, so giving this solution a different symbol means nothing

If I were to have a forumula that had somewhere along the lines an X that is 7/0 and later have X*0, the /0 and *0 would cancel each other out and I'd get my number back. But if I evaluate 7/0 to Nullity, and then multiply it by zero, my number is gone.

Stay at home mom
Renaming the problem is NOT a solution. The guy is a total dingbat.

it's hard enough with 10 numbers to remember I DONT WANNA REMEMBER ANOTHER NUMBER

You have got to be kidding me. Looking forward to seeing Reading University maths application plummit.

Funniest BBC article ever. I hope this guy has a lot of savings so he can retire to an island somewhere.

division is basically subtraction. For example: 4/2 means how many times can you subtract 2 from 4, in this case 4-2=2, 2-2=0 (so the answer is 2). Now if we look at division by zero, for example 4/0, this is basically asking how many times can I subtract zero from 4? The answer is: 4-0=4,4-0=4,4-0=4,4-0=4 .... This goes on forever, it does not end .. meaning its infinity it is not the largest number possible. In fact there is no largest number. Lets say x = the largest number possible, then what is x+1? As for 0/0, it should equal one. Because it asks how many times can you take 0 away from 0, 0-0 = 0 (that's 1 times)

Okay, but how do you want to dividied the new number? I think, then there is the same problem again...

If anyone with any mathematical background was asked to evaluate the expression x/x, they would say that x/x=1. EOF.

The Nutty Professor
If I have 2 marbles and I divide it over 0 persons then I haven't lost my marbles, right? I still have'm. But according to mathemagicians I end up with nullity and loose my marbles?

Dr. Andrea Armani
Mark Skerritt answered this problem (along with all of the people who proved this proof was incorrect) - use Calculus. If this guy is a Dr. in a comp sci department, he should have taken calc. and this is the first problem that is addressed in any calc course - solving 0/0 using summation. On a side note, Newton developed Calculus. So yes, Newton solved this problem. I don't know who the other two doctors are who vetted this proof, but they didn't do a very good job.

This makes me laugh . did he do this for show !? " it's that easy" ...

take a piss
So what is 10/0? How do you approach nullity? does nullity come before zero?

"I wrote the whole lot down as logical rules or axioms. Dr. Andrew Adams from Reading University and Dr Norbert Voelker from Essex University helped me develop the axioms. Norbert translated the axioms into higher order logic and used a computer to prove that they are consistent." Both of these people are computer science "Dr.'s." Just because you can write your axioms in Prolog doesn't mean it doesn't contradict everything we already know about mathematics. Try lambda calculus.

Josh Jelin
Dr. Anderson doesn't really know what he's talking about. Defining a number as the solution to a problem doesn't solve the problem. Mathematicians thought of his solution hundreds of years ago but instead chose to leave 0/0 undefined because “nullity” is useless. This would be exactly the same argument as saying we “solved” the square root of -1 by renaming it to i.

Yes - I understood it back in 1978 when my geometry teacher explained that it was used to create the Cartesian Graph (the Y-axis is div0 - a line from negative infinity to positive infinity).

The international standard IEEE 754 defines representations for Infinities and for NaNs (Not A Number)s which accomodate Dr. Anderson's theory. So what's new? Computers may crash if they haven't been programmed to allow for these exceptions to the norm (and not many do in my experience) but they could do.

I wouldnt view 1st alien contact if i had to use real player to see it.

Burt Wurstheimer
The wurster says: Stupillity. Reduntillity.

If you would like to do an article on me, I also figured out a novel problem.. Using the same logic, and inspired by Dr. Anderson. The solution to cold fusion. It's easy! See, E=mc^2. so mass can be converted to energy. To do this, you need specific conditions for the reaction to happen. I have come up with a new term "energity". by adding mass + energity = electrical energy! Not only does it produce energy, but it is electrical energy rather than heat and electromagnetic radiation. This means no conversion is required, you just take some material (garbage for instance) and add energity, and you get electrical energy. pretty easy huh? Better yet, computers can easily solve the equation without displaying an error message.

Mathematicians have been "joining" the ends of the number line with a "point at infinity" for years. It's an important part of the theory of elliptic cryptography. This is nothing new - just a coat of whitewash and a different name over an existing idea.

A. Supporter
I know nothing about this

dave p
If Dr Anderson insists on putting nullity there, then there is no room for i. Cancel that Complex Analysis class matron.

Non Scientist
All this mathematics stuff is great, just a shame most cannot spell. Now there is a 'real' problem.

Major Flaw in his "problem solving"...he is applying the rules of the real numbers to a set that is "outside of the real numbers". x^0 = 1 in THE REAL NUMBERS since nullity is NOT A REAL NUMBER you cannot apply the same rules!!

So could the professor please explain the properties of nulity under addition, subtraction etc...sounds like the "bottom" value from lattice theory to me ... but that's nothing new. Next week, Reading Uni discovers set theory

Craig Bruce
This sounds a lot like what is implemented in IEEE floating-point numbers (which are used on all modern computers), except that it gives "nullity" the name "NaN" for "Not a Number". NaN operates basically like a trap in that any operation involving NaN will produce NaN as a result. Of course, I don't really see how you keep airplanes flying when every flight-control calculation results in NaN or "nullity".

Zero divided by zero has always been defined as zero. A-level maths. The fact that computer's processing microcode doesn't handle division by zero is irrelevant. Everyone checks for zero in their code and avoids it. Computer Science O Level. So - this astounding revelation is irrelevant to any one with a moderate education. Well done the BBC - have none of you got any Science qualifications?

Nullity Master
BS Theory Divided by the 0 number of people who are digging this story equals the nullity chance anyone will ever take this Dr seriously again.

Who is this guy who says I can't solve problems? Heck, I've been dead for more than 2500 years, so where does the 1200 years come in? Go meet my mate Giuseppe Peano who first wrote down the basic axioms of arithmetic. He'll tell you whether there's a Nullity or not!

Define nullity as 42 and you have got the answer to all your x/0 questions :-)

this is retarded... i've been setting nulls for years when division is by zero... how does this equate to solving a problem?

Dr. Anderson: I'm confused as to why you can rewrite 0^0 as 0^(1-1) (or why you can even write 0^0 at all) from your list of axioms. Could you rewrite this proof without any shortcuts and annotate each line with the axiom used from

jack welch
I think he may be on the verge of greatness! Nobel prize?

It's MMD!!! Mathematics of Mass Destruction. We must now send in the troops.

I agree with PK and similar responses. For some 60 years I have always understood that 0/0 is any number. 'Nullity' simply means any number. I would love to see any application of the concept of nullity. The children must be very confused.

just some professor of physics
Isn't it obvious - this guy is a lunatic. If he really had something new, he would be publishing it in a peer-reviewed mathematical journal rather than trying to peddle it to children. My god, are people so gullible. I guess some are, because after all Reading University hired him, the BBC put him on the news, and the school at Highdown let him teach their students.

I told you this day would come.

Dr. Anderson should read "Nonstandard Analysis" by Abraham Robinson. Robinson came up with a consistent algebra that employed classes of infinitesimal and infinite quantities about 50 years ago. Using that algebra he showed he could create the same calculus we all know and love, but without using limits.

This man is a computer scientist, not a mathematician. I can't believe these kids are buying into to this garbage. I also can't believe that this man can believe that nobody else has ever thought up of giving a new damn name to an already existing concept, especially considering how NaN already exists and he is, supposedly, a Doctor of computer science. NaN works well, this is simply a stupid relabelling. Of course you've 'solved' it, you defined it that way in the first place! I dare him to send his into MIT, Cambridge or Clay, they'll shoot him down in seconds. BBC you should be ashamed to have featured this, slow day for news was it?

Cameron Kenneth Knight
Although I do not believe that Dr. Anderson's theory holds water, to the people who ask to show the number in binary really need to study the IEEE-754 standard. The IEEE-754 standard specifies binary representations to 32, 64, 43, and 79-bit floating-point numbers. In this spec allows for the numbers infinity, -infinity, and NaN. Since NaN is essentially what Dr. Anderson descibes as nullity, one could use that as its repesentation. Also, NaN is defined when the exponent is 2^e − 1 and the mantissa is non-zero, which covers many, many numbers. One could instead define NaN to be where the mantissa is non-zero, non-1 and nullity to be where mantissa is 1. Integer representation of nullity (and also infinity and -infinity) is typically not needed, although if you were to use a modified integer set, it could be done. E.g. looking at an 8-bit integer typically defined as -128 to 127, one could define 127 as infinity, -127 as -infinity, and -128 as nullity.

Some of the people bashing this should learn some basic maths. Others should read the papers he has written. Still others should learn to read the first line of the article above, which is fairly clear that Dr Andersen works at a university, and not a school. Unfortunately the ill-informed comments so outweigh any useful criticism it is hard to find genuine, sensible, objections. Those with sensible objections would probably be most welcome to hunt down Dr Andersen's email and present them to him - so far none of the mathematicians who have tried have managed to show there is anything wrong with transreal mathematics (well... I pointed out that his earlier version was lacking negative infinity) The comments about NaN often confuse infinity with what Dr Andersen is calling nullity. Some programming languages define infinities as well, however, and from this perspective I believe some of the criticisms are valid.

Is he suggesting that coconuts migrate?

Math Guy
Sad reflection on the state of scientific erudition in journalism (which seems to be closer to zero than to nullity ;-). Why even call attention to this vapid, empty theory (not to mention the preposterous claims that the problem was 'unsolved'). If anything, the problem was ignored, because it is of no significance. Shame on you BBC.

Mark Wagner
"Nullity" is hardly a new concept in computing. The IEEE standard for computer mathematics defines three "non-numbers" that can result from an operation: positive infinity (the tangent of 90 degrees, or 1/0, or any of a number of other operations), negative infinity (the tangent of -90 degrees, or -1/0, or any of a number of other operations), and not a number (0/0, or infinity/0, or -infinity/0, or other operations that are not well-defined). Calculus-level mathematics has been able to deal with 0/0 for a little over three hundred years. It all depends on where the zeroes come from: 0/0 could be 0, or 17, or any other number. There's a technique called L'Hopital's rule for determining this.

Many of the operations Dr. Anderson performs to "prove" this (such as the algebraic principle that (a/b)^{-1} = (b/a) ) _assume_ the basic field axioms. Of course, these axioms assume that aa^{-1} = 1 only if a ≠ 0. Dr. Anderson first has to show that if you extend the field axioms to include 0^{-1}, then the usual algebra applies to it. And he hasn't.

See for James Anderson the estate agent (top of the list under Google). Now all becomes clear!

Mahesh Sooriarachchi, what you propose is (an apple)/0 = (an apple) which means basically that 0 = 1. Which better not be the case. dividing by 0 cannot exist or math doesnt work.

Ashley Cole
I am currently studying mathematics at A level, and this cannot be real. Surely he cannot jsut make up a new number? If anything it should be under imaginary numbers? I disagree with what Dr James Anderson has proposed, as you cannot divide any number by zero, as there is nothing there to be divided by! It cannot be done.

So he worked out that the zero to the power of zero was zero and gave it a name?

John Meagher
Dr Anderson may have the right idea, but the naming convention is a little off. According to Dr. Anderson, when you divide by zero, your answer goes to infinity (+/-), and covers a range of numbers starting with the next number beyond the numerator to infinity. However, "nullity" indicates a NOT anything, even though dividing by 0 is a NOT NULL answer. I'm not a math wiz, but it would make sense to me if dividing by zero is still a controversy, then "nullity" would be a "not defined". By placing "nullity" outside of the number line, indicates the answer is still unknown. If the answer is unknown, then "nullity", with all that the name implies would be an inappropriate name. "nullity" would be appropriate, if the affect of dividing by zero results in zero (null). This tends to make more sense to me: 0 x 5 = 0 0/0 x 5/0 = 0/0 5/0 = (0/0) / (0/0) 5/0 = 0 If 0 follows the behavior of small numbers, then the answer is infinity. If 0 is treated as null, then dividing by null is the same as dividing by 1; No affect on numerator as a given number over one. In either of these cases, "nullity" is not an appropriate name for a not-null result.

Chuck Norris
Only Chuck Norris could divide by zero. And I've done it twice.

What a bunch of baloney! The problem with 0/0 and 0^0 is one of uniqueness, not of simply needing a name for them.

my digital camera tries to divide by zero quite often, i have to take the battery out and reinsert it as a workaround. dr anderson's simpler solution would save me that trouble! he should let nikon know quickly!

Ex of Reading
Message for Kevin Warwick: Be afraid, be very afraid!

The problem is that dividing by zero is not a problem. It's not an operation, just as jumping without lifting your feet off the ground is not jumping, or eating without opening your mouth is not eating.

This is total crap. Of course the students are confused. It's entirely wrong! I can construct a vast number of examples where 0^0 is one, or zero, or one half, or a variety of other values. Can I compute something with this "nullity"? I think not. 0/0 is an undefined form, and there are an infinite number of possible values for it. This is nothing but some computer science PhD delving into the world of number theory when he really shouldn't, and all it is going to do is confuse the students he teaches, especially when they get to a real maths class.

The Real Numbers form a complete ordered field. Let's just look at how well Nullity fits into the Real Field. FIELD INCONSISTENCY The Real Numbers form a field. In it, every number except the additive/multiplicitive identity has a unique distinct inverse element such that x*x`=E. What is nullity's inverse? Let's look at the multiplicitive inverse. Nullity's multiplicitive inverse would be 0/0 (it's reciprocal). By this result, either E=Nullity=0 or Nullity is not in the set of Real Numbers. If it is not in the set of Real Numbers, what set, group, ring, field, algebra does Nullity fit into? Would 10 Years kids be able to grasp a separate set of rules distinct from the rules they've learned thusfar? There's a reason this professor is teaching high school children... That reason is not flattering.

my name
and the square root of -1? i'll call it bob! it lies off the numberline, and i've just solved an age-old problem. want to join the problem-solving fun? just rename everything! it's easy!

How about encoding the video in a format that's not as worthless a $0/0... MPEG is an industry standard.

The next mask for 1/0, after Nullity, shall be Willy-Nilly!

Flash Cut
nullity =NaN(Not a Number) Do you think people are stupied???????????? Try again .LOL

Percival Sittingbourne
That's Numberwang!

Uhhh, Riemann Sphere? This guy is 150 yrs slow.

O Ramon
If you have nullity over nullity, does this mean that it is equal to 1? or would it remain outside the number series. If you multiply nullity by any real number is it still a real number, or is it nullity? If you multiply a nullity by an imaginary number, it it in either or both sets?

Computers have this concept already. It is called NaN. This guy should not be allowed to teach. His axioms=diddly/squat.

Eric (M.S. Mathematics)
I had an uncle who was a philosophy profressor (now deceased). For entertainment, he used to assert that there was an extra integer somewhere between 8 and 9. He'd tell everyone he was working on a proof named "the sneak" whereby he planned to line up 10 oranges and then, somehow, "sneak" the extra orange somewhere between the 8th and 9th one, thus proving there is an extra integer in there somewhere. He'd tell people about this and laugh until he had tears in eyes. Yet, somehow, his mathematics are more appealing to me than Dr. Anderson's. At least they're funny.

this is not a significant 'discovery' and should be peer-reviewed. his derivation [shown in video] contains two potential meanings for 1/0. the first is his infinity. the second is to ignore it while doing his 'solution', he says that 0/1 x 1/0 = nullity... this is ambiguous given his prior definition of infinity being 1/0. now, infinity multiplied by zero is nullity. on a side note. i would like to see his version of common algebra using nullity. 37/0 for instance. 37/0 = 37/1 x 1/0 = 37 x infinity ... but 37/0 is 1/0 x 0/1 x 37... this seems to be not clearly defined in terms of behavior. this seems problematic as we are now back to the original division by zero being undefined if multiplication is not consistent.

Erik Mesoy
This has more holes in than Swiss cheese. By his math, 1 = 1/1 = (1/0)*(0/1) = (1/1)*(0/0) = 1*Nullity. Hence nullity must be the multiplicative identity element, nullity=1. I also note that this is filed under "people" not "science", and the man does not have a math degree but a comp sci degree. Another hole: (a/b)/(c/d) = (ad)/(bc), so (0/0)/(0/0) = (0*0)/(0*0), and thereby nullity/nullity = nullity. Divide by nullity on either side and you get nullity=1, multiply by nullity on either side and you get nullity=nullity^2. Also, this breaks mathematical groups and rings too. 1+nullity=? 1*nullity=? 0*nullity=?

infinity/infinity is not equal to 1 any more than infinity-infinity=0 . Infinity cannot be treated like a regular number. Just because we don't know what nullity/nullity is doesn't mean the idea is pointless. Let the scientific community sort it out before you all dirty your pants in frustration.

Disgusted in Vegas
He's actually teaching this to students as legitimate "mathematics"?

This is a load of crap. Saying dividing by zero results in something that is not a number (nullity) solves nothing and breaks mathematical closure. It is shameful that this idiot is allowed to screw all those kids up. If he has a degree in mathematics it should be immediately revoked, as well as his teaching credentials.

Free Will ::= Nullity
In his works, Mr. Anderson proposes that a "free will like ours" does actually exist. If so, then nullity actually does exist. However, both are just artificially making up something that is actually undefined. No problem solved, only postponed to a future representing some instance of nullity.

Nick Wilson
What 'problem' is caused by division by nought being undefined? How does this help anything in any way? You can trivially define it any way you like, but so what? This causes big problems - his axioms must be a total rewriting of all our basic arithmetic. This is very stupid. PS lots of people seem to think (oddly) that 1/0 = infinity -- THIS IS NOT TRUE. 1/0 != infinity. It is undefined. lim_{x \rightarrow 0} =\infinity (in words: the limit of 1/x as x tends to 0 is "infinity", but has NO VALUE at x=0) We use a lot of different ideas when we talk about "infinity". The calculus idea of an arbitrarily large number (ie 'limit as x tends to infity' or '1/x tends to infinty as x tends to 0') is different from the idea of, for the instance, the number line being "infinite". The transfinite numbers (\aleph_{0}, etc...) are yet another different meaning of the word infinity. Did this idiot get his Doctorate in Geography or something? I can't believe no-one has told him that throwing an exception on division by zero is good - would we rather have the plane plough into the ground because it ignores the error? Catching exceptions is good software design, not ignoring the problem by renaming it.

Responding to "Pythagoras'" question about whether or not 2/0 is twice as infinite as 1/0. Although I don't know exactly if that's correct, it is mathematically correct to say that some infinite sets are larger than others. Consider the following three sets of integers: a) 0 to +infinity; b) 0 to -infinity; and c) -infinity to +infinity. If you think of it in terms of the lines growing away from 0 then it's clear that set "c" is twice as big as either set "a" or "b". An even more unsettling example is the set of integers from 0 to +infinity versus real numbers between 0 and 1. If the first set grows at the rate of 1 integer at a time, but the real number set grows by halves (ie, 0 & 1, 0 .5 1, 0 .25 .5 .75 1, etc.) then the set of real numbers not only grows faster than the integers but it grows infinitely faster. And so, it is a fact that some infinite sets are larger than others. I know, it threw me off at first too, but now it seems reasonable (which is good or I would have failed the class where we learned that - although now it only comes in handy for showing off).

Captain Anon
Insanity! 1/2 is equivalent to 1*(1/2) 2/2 is equivalent to 2*(1/2) 0/2 is equivalent to 0*(1/2) Now m/n is equivalent to m*(1/n) 0/0 is equivalent to 0*(1/0) Everyone knows 0 * (anything) is 0. So, "anything" includes all numbers, real and imaginary. a. 1/0 = infinity b. 0*(1/0) = 0*infinity c. 0*inifity = 0 Hello?

That makes no sense at all. 0^0 is not defined, therefore 0/0 is not defined. You can't prove anything by confusing people with wrong facts.

Makes calculus a whole lot easier too. lim(x->0) x/sin(x) = 0/0 = NULLITY!! Oops. Looks like we'll have to rewrite all the math books in the past 500 years.

much ado about nothing

Egon Ipse
This is funny! To all people posting here: YHBT. YL. HAND! Just look at his grin on the video when he claims that the reciprocal or 0 is 1.

I hope Dr Anderson gets a huge monetary prize for his discovery so he can retire and stop teaching children. What a shame, where this world is going...

OK he's just a very newb at comp-sci math professor who thought he came up with something original. I'd bet it wasn't his idea to go to the media, though. Computers CAN represent -/+ infinity, and often do. Also, what is infinity * 0? ZERO. That's why dividing by zero makes no sense, since division is the logical converse to multiplication. The problem this article raises is exactly what kind of crap our school systems can shouvel to kids. I am not religous, but I was taught at school that evolution was "THE WAY" even though it's just a THEORY, and I'm pretty darn sure that's not how true scientists would want it.

Great. This guy has spent all his time coming up with another symbol for infinity. I could produce an equally useless symbol, oneity, for the result of a number divided by itself. Is that groundbreaking? However, I suppose it does account for all those times planes have dropped out of the air. It wasn't high turbulence or some sort of storm. The plane simply tried to divide by zero.

Steve Q.
All maths problems are easily solved if one wishes to simply make up a new character to place on the right hand side.

So, tell us more numbers on this new number line, sir! You've given us a number that can be any other number (as where x is any number x*0=0, so 0/0=x, which means nullity=any number). How about a number that can do backflips? Or a number that can turn invisible?

"which solves maths problems neither Newton nor Pythagoras could conquer" How ridiculous! The reason neither Newton nor Pythagoras "conquered" this problem is because is because it has already been solved. 0/0 is undefined and calling it nullity does not change anything. How does this "new" theory of his provide a new answer for 5 * (0 / 0)? The only change now is that instead of getting "division by zero" computer exceptions one would get "arithmetic involving nullity" exception.

There already is a name for this number: QNAN Nullity is just a bad name that implies the opposite of what it is. A better name would be inverse nullity.

What happens when you assume...
First of all, don't trust a mathematician who issues false statements. 1/0 is not equal to infinity; similarly -1/0 is not equal to negative infinity. If we want to compute 1/0, we do this by taking the limit of 1/x as x approaches 0. So let x = 1, 1/2, 1/5, 1/10,000,... Clearly 1/x gets inifinitely large as x approaches 0. But what if we approach 0 from the other side (the left limit)? When you let x = -1, -1/2, -1/5, -1/10,000,..., then the limit of 1/0 approaches negative infinity. Since the left limit and right limit of 1/x as x approaches 0 do not agree, we cannot say that 1/0 equals anything. (Want to picture it? A similar example would be the graph of the tangent function. Tell me what the limit of tan(x) is at pi/2 radians, or 90 degrees.)

I invented the number 5. People seem to like it.

J. A. O. Ekberg
The problem with this is not that it's wrong or useless (it's not). It's just that though I have never seen formal proof of it before, nobody ever severely doubted that arithmetics including +infty, -infty and "indeterminate" can be axiomatized. Talking about such things at schools is not a bad idea; renaming "indeterminate" into "nullity" and claiming this is something revolutionizing is quite another thing. In terms of novelty (though not usefulness, perhaps), Jesper Carlström's wheel theory is much more interesting.

Ron Larham
Computers can divide by zero if the arithmetic is implemented correctly, 0/0=nan, 1/0=inf, ... by the way nan means not-a-number.

Jim Belcher
This is too much of a theoretical abstraction. The proof of its validity is likely to lie in finding a practical physical application. Mathematicians are know for abstract ideas that are proovable only on the blackboard. OK, so we can do it on paper, so what?

Every mathematically inclined person is probably groaning right about now. This is utter nonsense. The theories of 0/0 have been worked out for ages -- there's no mystery here. You can't know anything about 0/0, you can only say something about the limit as you approach this state from along a continuous line. Go look up L'Hopital's rule. You can't even say infinity"nullity. Heck, you can't even say infinity=infinity. There are different classes of infinity. About the only meaning "nullity" could have that would be reasonable is "undefined." Which, OMG, has already been used to define this state. About the most he could be credited for is inventing a new symbol for the word "undefined". Utter rubbish.

This guy is just assigning a symbol to something that still isn't a number. It's like me renaming the Sasquatch a "writing desk", pointing to a desk, and claiming that it's proof that the Sasquatch exists.

Adam Setzler
1/0 = Infinity 23/0 = Infinity 37/0 = Infinity 419/0 = Infinity 2305/0 = Infinity 12904/0 = Infinity 349002/0 = Infinity . . . Infinity/0 = Infinity Infinity = Infinity Your mom.

Cambridge Maths PhD
Having just read his papers, (and as other people have suggested) the symbol Phi is nothing more than a shorthand for "undefined". He lists his axioms which are easily understood with this understanding. This really is a second-rate piece of work. FORTRAN already uses the system he is advocating (Phi=NaN).

Hint to the BBC -- talk to an actual mathematician before publishing such a dreadful piece. We're really quite approachable, and perfectly happy to explain why this is silly.

Dr. Anderson obviously knows nothing of modern algebra. There is a very concrete reason why division by 0 is impossible, and if he wishes to make it possible he must also be willing to find a replacement for the foundations of much of mathematics. The real number line is a field, and it is not possible to have division by zero, the additive identity, in a nontrivial field. You can't just make up a new symbol and perform a handful of mindless operations on it to solve a "1200-year old problem". If he wishes to be taken seriously in the realm of mathematics, he must provide a radically new algebraic structure within which his nullity may exist. I don't claim that such a feat is impossible, but until it is accomplished, his "result" is illogical and should be labeled as pseudomath.

This is a good lesson for all who listens to "scientists" who preach global warming... Thanks professor

This is absolute crap. Who hasn't thought about replacing the concept of division by zero with some symbol while they were learning about replacing the square root of negative one with i? If this is a breakthrough, I should take over this guy's job. At least i has applications in the real world.

Utterly Confused
So James; you say: 0^0 = 0^(1-1) = 0^1*0^(-1) = ... = nullity. What about: 0 = 0^1 = 0^(2-1) = 0^2*0^(-1) = (0*0)*0^(-1) = 0*0^(-1) = 0^1*0^(-1) = ... = nullity.

most computer programs will catch the Division By Zero error and execute code designed specifically for such an eventuality. It's very very unlikely that programs will crash airplanes or stop a beating heart just because it hit a Division By Zero error. Software testers always test this eventuality and watch how the software behaves well before it goes to market. All Dr. Anderson did was put a name to a concept that's otherwise known as the Division By Zero.

Somehow this whole article feels like a ploy to get other people to do Dr. Anderson's job for him. Numerous people have pointed out the flaws in the invention of "nullity", and a few have suggested more effective functional alternatives (such as my earlier one, shown below because someone had the bright idea of posting replies in reverse order). Keep an eye out, as he may publish a paper in a year or two taking credit for ideas that appeared in replies to this article.

[Using the end of this message to see if HTML code may be planted directly into responses to create paragraphs. Simply typing carriage returns doesn't work.]

Paul Wells
Everyone should know that the BBC only likes arts and soft science programmes - so reporting something like this makes them feel they understand maths.

Andrew P.
I'm no mathemetician, but just at first glance I have problems with this. I guess one of my biggest "problems" with that he appears to be treating infinity as a number. Infinity is not a number, but a concept. He has that 1/0 = infinity and -1/0 = -infinity. That's not quite right, because it's actually: lim x->0+ for 1/x = infinity and lim x->0- for 1/x = -infinity But at x = 0, 1/x is undefined. There is no simple algebraic equation (a+b, a-b, a*b, or a/b) such that the answer is "infinity". If you then argue that using limits you can say that his axioms hold...I would again disagree...because lim x->0 for 1/x = +infinity AND -infinity (depending on which way you approach zero). (same for -1/x) If you do decide to treat infinity as an actual number, then the only way his axioms actually hold is if infinity = that means 1 = -1. (not to mention countless other areas where treating infinity as a number messes things up...)... So if the axioms don't hold, well, anything you use those axioms in really doesn't hold much water...If i'm wrong on this, feel free to correct me...

Jeff Pegg
This is the stupidest thing that ever got attention! Period! You aren't doing anything innovative, you are just trying to get your name into the books. And a quote from the article is the worst. "We're the first schoolkids to be able to do it - that's quite cool," added another. You are like the first christians to be deceived.

There's too many comments likening i (sqrt(-1)) to this new Nullity concept. The difference, of course, is that factors i can be plotted as a single point on a cartesian plane (it represents the non-real quadratic roots, which are useful in solving some problems) whereas nullity would be plotted by colouring the entire cartesian plane. There's lots of other high-fallutin' words flying around here too: non-euclidean geometry, transreal arithmetic. If this stuff is so theoretical that someone with an undergraduate background in mathmatics can't see how it applies to problems he's familiar with solving, why primary school pupils? Have they have evolved some extraordinary capabilities which allow them to apply non-real mathematics to the real world? Or does it just make a cute picture to launch this non-practical theory?

My first problem is his assumption that 1/0 equals infinity, and -1/0 equals negative infinity. 1/0 does not equal infinity. 1 divided by an infinitesimally small positive number is equal to infinity. 0 is not an infinitesimally small number. To make a random example, consider the mass of an "object". If the object has an infinitesimally small mass and a nominal volume, its specific volume (inverse of density) is considerably large (approching infinity as the mass gets smaller). If the object has a mass of 0, THERE IS NO OBJECT. Thus a measurement like specific volume would be undefined, because the object doesn't exist.

Anonomous coward
This is exactly the same as saying that the square root of -1 is i or whatever else you call it. It would be easier to just keep it as (0/0) in equations without giving it a symbol (that is already in use). Waste of time.

With the right assumptions you can prove anything to be true...even if it's completely false and/or inconsequential. 1/0 is not infinity. 1/x as x approaches 0 is infinity. They are two very different things. Faulty assumption = pointless proof.

John Meagher
Dr Anderson may have the right idea, but the naming convention is a little off. According to Dr. Anderson, when you divide by zero, your answer goes to infinity (+/-), and covers a range of numbers starting with the next number beyond the numerator to infinity. However, "nullity" indicates a NOT anything, even though dividing by 0 is a NOT NULL answer. I'm not a math wiz, but it would make sense to me if dividing by zero is still a controversy, then "nullity" would be a "not defined". By placing "nullity" outside of the number line, indicates the answer is still unknown. If the answer is unknown, then "nullity", with all that the name implies would be an inappropriate name. "nullity" would be appropriate, if the affect of dividing by zero results in zero (null). This tends to make more sense to me: 0 x 5 = 0 0/0 x 5/0 = 0/0 5/0 = (0/0) / (0/0) 5/0 = 0 If 0 follows the behavior of small numbers, then the answer is infinity. If 0 is treated as null, then dividing by null is the same as dividing by 1; No affect on numerator as a given number over one. In either of these cases, "nullity" is not an appropriate name for a not-null result.

so if a planes computer system divides by zero and crashes, we're all gonna die BUT! if it divides by nullity and crashes, we're all gonna die. wait...

Many people posting here are showing a lot of ignorance about mathematics. It has been known for a long time that 1/0 = infinity and 0/0 is undefined. Conventional computer arithmetic can not cope with this. What Dr Anderson has come up with is a method for allowing computers to do computations involving these operations. However, it is so obvious that I doubt it has not been done before.

James H
A lot of people posting here are showing a lot of ignorance about mathematics. It has been known for a long time that 1/0 = infinity and 0/0 is undefined. Conventional computer arithmetic can not cope with this. What Dr Anderson has come up with is a method for allowing computers to do computations involving these operations. However, it is so obvious that I doubt it has not been done before.

A lot of people posting here are showing a lot of ignorance about mathematics. It has been known for a long time that 1/0 = infinity and 0/0 is undefined. Conventional computer arithmetic can not cope with this. What Dr Anderson has come up with is a method for allowing computers to do computations involving these operations. However, it is so obvious that I doubt it has not been done before.

Infinty and Beyond
Throughout history the equation (n/0) = infinity. Surely he has just changed the name given it a new symbol. PS can i have a reserch grant for discovering this nugget of information.

Reid Nichol
All this guy has done is redefine what the real number line is and a few numbers. Let's go over his major mistake: inf \neq 1/0 To get this one must do: lim_{x->0^+} 1/x Similarly for -inf. But one must note that if we approach 0 from the left then the sign flips. But that's another story. What he did was an operation that was undefined and define it without exploring any of the implications. This guy is playing with a NEW number line of his own invention. Also, this NEW number line has not been shown to be mathematically consistent in any way shape or form. This guy should be embarrassed to publish this.

Mr. ner axiom
nullity = all the peoples in this blog.

taxi driver
Get a real job giving handouts to immigrants instead of wasting your time growing a beard and mumbling like an Open University presenter on BBC 2 in 1983.

A Brit
What is math?

These poor kids. I just hope none of them put this on their college applications under accomplishments.

So.. it took this long to invent another imaginary number? The square root of -1 is "i", and now we have another. I don't see anything big in this, just semantic gymnastics. Well done to this guy for selling it well though...

Extra dimension?
The number line is linear. Add another line and two number lines gives us two dimensions. And finally add a third and there is our 3rd dimension. Now according to this "But Dr Anderson has come up with a theory that proposes a new number - 'nullity' - which sits outside the conventional number line (stretching from negative infinity, through zero, to positive infinity)." So does this mean he found an unknown dimension?

Dan Jones
My calculator doesn't give me an error when I divide by zero, it just returns "undef." It looks like Texas Instrument figured out the solution long before this crackpot!

Patrick Weber
His interpretation is completely outside of the rules of mathematics1 How can this be useful1 If the final answer to a problem is "nullity" what does that mean1 Does it get us any closer to understanding than 0/0; no1 What is "nullity" times 4- He had kids memorize that 0/0 could be written as a 0 with an I through it1 They have done nothing that Newton couldn't1 Throughout this post I have been using 1's in place of periods and -'s instead of question marks1 I just wanted to let you know that I have done something that Shakespeare never could1 I am awesome1

Ian Bremner
Hardly news since mathematicians have been usng a similar method to represent the square roots of negative numbers, at least they're hones about it and define the root of any negative number as 'i' - short for 'imaginary'

I am but a child and think like a child. I am told that to solve the equation 2x = 4, I can divide by 2 to get x = 2. Thus 2 \times 2 = 4. Now I am told that I can divide by zero. Dr Anderson says so. So to solve the equation 0x = 1, I must divide by zero to get x = +infinity. So 0 \times +infinity is 1. Now let me solve the equation 0x = 2. Then I get x = +infinity. So 0 \times +infinity is 2. Now let me think. Oh yes then 2 = 0 \time +infinity = 1. Oops! Please Sir, what have I done wrong.

If this man thinks he is some sort of mathematical prodigy, he needs to go take his medication. And teaching this 'stuff' to kids is just outrageous. He doesn't actually DO anything other than say 0/0=0/0 and then give it a name, ha. What a joke.

This doesn't make sense. "Nullity" and zero may be different entities, but zero is the number that appears on the number line.

He just "solved" the case 0/0, but not n/0 by using (valid) algebra rules. His "proof" is like saying "8/4" equals 2, so everything else divided by 4 equals 2. This "nullity" is just another alias for 0/0, which has been invented many, many times before.

yeah because ya know, making your own "number" up and saying it's a solution is really mathematical.

If one of his pupils came up with that in class, I am sure Dr James Anderson whould of told them off for wasting time. The alternative name to Nullity is called Stupidity.

Whats the difference between infinity and zero really ?

Your calculus professor would be very sad. =( Please teach the kids real mathematics and not some hoopla. Don't waste their time.

If anyone has read down this far... I believe 'Sam' has it. In the "Proof", which is more of a sort of verification, (1/0)*(0/1)=0. But (1/0) is Nullity. So, in essence, he's using Nullity to prove Nullity. A big no-no.

Why does the symbol for nullity look like a capital phi? And this is absurd.

Confused at Meaning
How about we just define 0^0 as some number? Then I can prove that 0^0 is that number that we defined. Yeay, I just solved the 0^0 problem.

I've seen an article on BBC saying that UK does not have enough scientists but I didn't realized until now that it was such a huge problem ...

Sorry, at what stage did this become news worthy? Who exactly went out and scouted this story? Is this the future of TV, Web, Radio current affairs and news programming? Dump this tripe and report on something that actually MATTERS! Otherwise I fear we will all end up being divided by zero into an infinite state of apathy and incredulity towards the seemingly ever expanding "anything ‘ul do" news culture....

Making up pretend numbers = I ARE MATH SMARTNESS. I hereby propose a new number that is to be called "squnch." It has a value of 23, -78, Pi, and the color orange; simultaneously. Also, it is lemon-scented. I suspect that the proper use of Squnchificonics will be able to solve all sorts of previously impossible mathematical problems, as well as leaving behind a fresh, invigorating scent. Grant money now plx.

By the way, I lived around 500BC, so the problem is more than 1200 years old. Other than that, I can't fault this article.

Rusty Shackleford
What an utter waste of electromagnetic energy this story is occupying right now. Amazing. I wish my boss worked at the BBC.

How does this differ from i=SQRT -1, i is an imaginary number ??? Used in Calculus for YEARS !!!

Bryan Wagner
This theory is like playing a game of "I win". Here's a generic algorithm: Let A be a proposition. "I win", therefore, "I win"! Oh my!!! P = NP!!!

seiko flossberg, you just didn't get it, did you... read the above article again and try to understand

How can pacemakers divide by zero? I reacted, too. And of course, it's a MAN who comes up with this brilliant, easy idea.

Arvin Dargfarth
Too bad you have the Moore and Anderson bits on ram files.. Could have been interesting otherwise.

Dr James Andersen
To continue with my truncated comments below: the number 1/0, is, by my definition, > 2/0 or 10/0 or 10000/0 or indeed, 0.2/0. Therefore it follows that 0^0 = 0/0 - a class of 10 year olds has followed this. If they can it should be easy for others.

Cambridge Maths PhD
In fact there are ways to deal with infinities arising from division by zero (in some sense), but, as far as I am aware not by adjoining the real line with a new number (to do so looks suspiciously like taking the real section of the Riemann sphere). The matter of 0/0 is still undefined in all these approaches (the definition of a system of arithmetic is that of a mathematical field, and the field axioms leave this undefined. One would have to use a different definition of arithmetic if you want to get around that). Mathematicians in the last century discovered a new system of arithmetic that is a generalization of the real numbers, these are the surreal numbers (there is quite a large literature on the web). Related to this is non-standard analysis which makes use of similar quantities to develop an algebraic calculus. Roughly, real numbers are defined by a Dedekind cut, that is by taking the rational numbers on the number line and diving them in two. Surreal numbers are defined similarly though in terms of a cut of the surreal numbers themselves (so it's a recursive construction). The surreal numbers contain non-zero numbers that are smaller than any real number, and others that are larger than any real. In this way infinitesimals and infinities can be dealt with algebriacally (an infinitesimal might easily be mistaken for 0 if we thinik only of the real numbers), though division by it is still well-defined. All very elegant, but whether Dr Anderson has rediscovered this or someting similar, I wouldn't like to say as I can't download his proof.

Fairly easy from the article. I would love to see the paper he produced though. It will make our maths considerably different to before.

PC user
If Dr Anderson is from CS department would he not already know that PC's have NaN for divide by zero problems?

Dr Roy Johnstone
I am a lecturer in the Department of Mathematics at Reading University. I wish to distance myself completely from the utterings of Dr Anderson. He is NOT a member of the Mathematics Department and cannot represent the views of the Mathemtics Department. The idea that dividing by zero has been an unsolved problem for mathematicians for hundreds of years is laughable. His `solution' is nothing more than the unnecessary use of terminolgy to indicate that a division by zero has been attempted. The promotion of his ideas to school children is likely to confuse rather than enlighten them. He is being very irresponsible.

Tungsten (born in a Meteor)
If Dr Anderson's axioms are indeed consistent with arithmetic as he claims, then you can use his axioms to prove in 3 lines that Nullity = 1 and Nullity = 0.. in other words that 0 = 1. I'm glad that most comments below are critical, it shows that people can still think for themselves and not be dazzled by semantic sleight-of-hand. In other words, this is grade-A applesauce.

Absolutely bad theory. Has nothing to do with real science. Demonstrates very poor level of the guy. The theory will completely fail if it is used in calculus. Indeterminate forms of type 0/0 (when one looks for limit of quotient of two vanishing functions) cannot be evaluated like some universal symbol. That's where calculus started its development (by smart guys, not like this one). I want to see him flying in a plane desinged using his theory. And his (antiscientific) theory is really confusing for 10-year children. One should forbid him from teaching in school - otherwise he may spoil a future mathematician or engineer.

Kartik Krishnan
If this was the case a zillion pace makers would have already failed and aircrafts crashed...thereby killing people. Also computer systems are quite advanced to handle infinity (this is what we get when we divide a number with zero)As if you see the smaller the fraction of the number you divide a number with the result is a huge number (so infinity)

The fact that he preached this drivel to kids instead of Mathematicians pretty much says it all. They were the only audience that would not burst into laughter.

Doctor Science
I think he is making something out of nothing.

benjamin sanchez
what he says is not posible beacuse 0^0=e^(0*log(0)) and log(0) is undefinied at zero (goes to -inf), what he proposes is just a diferent notation to something that can't be done.

Imagine that, we solved a mathematical impossibility by creating another imaginary number (such as pi, i, and infinity).

Amazing breakthrough! Congrats. For all you university of reading computer science folk here is a nice patch to fix all the mission critical systems you're running! #define NULLITY NULL

Well this is great fun. Those who object to Dr Anderson having merely stated a tautology surely pay him a compliment, since all of maths is one big tautology: ie what follows from the chosen axioms is what follows from the chosen axioms. But the choice of axioms is a significant question; if those listed in Dr A's paper on transreal numbers do indeed contain all real arithmetic as well as have some extra benefits, then good on him. Unfortunately I am not clever enough to know if they do, so we should await some proper peer review of his papers before dismissing him completely. Wasn't the square root of 2 initially rejected as heretical? (I believe someone was killed over that heresy).

When a computer program tries to divide by zero it will be imformed by the operating system that this was an error and the program can use this information to avoid continuing on with some crazy result. Only poorly written software will actually crash. You can create a mathematical system whith whatever concepts you want such as infinity however this doesn't mean they have any relevence to anything in the real world Just my 2 Nullities.

Its not a proof. He's just saying that 0/0 is something and he calls that something nullity. Its like sayin 0/0 = x. Theres no actual value to it.

Richard Lee
Nullity sounds like just another way of saying "Damned if I know!". The Prof is attempting to create a new symbol where there is no need, we already have a suitible symbol and its already in common usage "?". Seriously though, has it not occured to anyone that 0/0 doesn't actualy have an answer because it is a nonsensical question.

Prof. Pedro Carvalho Brom
Ok. But as to explain these activities of the zero in complex plain? After all its the zero that transforms C in to R

Robert Newson
Clearly Dr Anderson is a weak mathematician. It's scandalous that he gets to teach this nonsense to schoolchildren. Dividing by zero is a problem because we define division, in normal mathematics, as the inverse to multiplication. There is simply no value that you can multiply zero by to reach any other value. 'Nullity' solves nothing, the man is a fool.

Mr Type Cast
All i can say is 0x00544e5543, Go figure! (the clue is in the name)

David E
Is this a joke? Basically you're saying that 1/0=A where A=1/0. Congratulations genius..

Maths Man
This is not maths. I've heard that this guy is a running joke in the University of Reading Mathematics department. Please check your stories with informed academics before making fools out of yourselfs.

Matthew Graybosch
When I studied maths in school, I was taught that the result of a divide-by-zero operation was "undefined". Dr Anderson's theory makes sense, but when I'm coding, I'll keep putting in code to catch divide-by-zero attempts and deal with them.

why don't they just program the computers to recognise zero as nothing? It's not infinite, it's NOTHING!!

i have a better word for it. how about flooglyflop? what a stupid article

He forget to name the "Theory"
It's called : "sensationalism". Dr Andersons "nullity" is not a theory nor some "new thing" let along any concept that could help software engineers, trust me. This is not a theory, just the mere introduction of a new symbol for something that already exists, and which obviously journalists fail to understand.

Master Dan
Breakthrough!!!! I have solved the problem dividing 2/3!!! Finally we dont have to wright it in fractions or aproximately 0.333333. My Great discovery is this 2/3=¤. From now on,insteead of writing 2/3, lets print "¤"! I cant wait for BBC to come knocking on my door!

I'm no mathmetician, but, not wanting to spoil "established mathmatical proof", surely all those who are saying "1/0 = infinity" have lost the plot haven't they? Surely that would mean that "1 = infinity * 0" and then "1 = 0"!?!?!

Someone with a degree
1/0 does not equal infinity. It is 'undefined', and for good reasons. Division is based on multiplication, where x/y = z also means that z * y = x, in this case infinity * 0 = 1, which is false, which obviously foils his axioms. Moreover, infinity is not a quantity, and is not allowed in arithmetic because you cannot apply all the basic principles to it. Example: a + b = c, a + d = c, then b = d. if infinity + 1 = infinity, and infinity + 2 = infinity, then 1 should equal 2...this is why infinity is not used in arithmetic. His 'theory' will not stand up for a second in the mathmetician world. Sorry you were all duped.

Bill Hannahs
What exactly is 240 times null? Get back to me when you figure this out. A new problem is created by the null solution in the value is passed... how is the computer going to handle arithmetic computations on null other than crash? Nulls are a real pain to work with as it is and usually you not only code to handle division by zero errors but also for errors involving functions on null which are frequently more difficult to write than for division by zero. This solution really opens a can of worms: you'd need to rewrite all arithmetic functions and most code which uses these functions and you would end up with an even less stable system than if you just dealt with the error properly.

Nothing new here. Old theorem, new packaging. Publicity stunt.

What's in a name? that which we call 0/0 By any other name would be just as false; So 0/0 would, were it not 0/0 call'd, Retain that dear falsehood which it owes Without that title. 0/0, doff thy name, And for that name which is no part of thee Take all my PHI.

So its invent a number time. In which case I propose that 2-1="dog" Discuss.

You can't use 1/0 in your equation to define 1/0. That's going round in circles!! No pun intended.

Clive Page
As many others have pointed out, most modern computer processors use IEEE 754 arithmetic in which 0/0=NaN. But he does have a point in highlighing the need for fail-safe software: the first launch of the Ariane-5 rocket by ESA failed because of a numerical overflow in the guidance system. The system detected it and switched over to the spare, which of course performed the same calculation, and there was another numerical overflow a few milliseconds later. The rocket had to be destroyed over French Guiana at enormous cost.

April Winterbottom
Sorry. It is still December.

That's not solving - that's a definition and a circular evidence. Nothing's been proven.

my friend's pacemaker divided by zero and stopped working 2 years ago. They did implement new technology where it wouldn't do that anymore.

Jacques Bourquin
There actually is some truth to this document. Let's suppose for a moment you have 1/0, (or 2/0, 3/0, n/0) which essentially equals infinity, remember that infinity is a condition, not a number, that's why we can say this, because we aren't expressing a finite quantity. So let's do some simple algebra and we get 0 = 1/infinity = means 0 = 1/(1/0) = 0/(1/0) = 1 = 0 = 1, so essentially by trying to express 0/0 as number you are saying 0 = 1. But wait, we learned in fractions that any number divided by itself is 1, but earlier we just said any number divided by 0 is infinity, so, which is it? Does 0/0 = 0, 1, or infinity? Therein lies the problem with 0/0, in calculus they call this an indeterminite form, because its value cannot be determined. Class dismissed.

Larry V
Initially, I thought this story was a joke article. Really. I looked around the page for something like "Today's funnies." Failing at this, I'm forced to accept that this is perhaps TRUE. This is ridiculous. Just making up a new number doesn't solve anything. We already had something that represents this sort of idea: "NULL."

"Thou shalt not divide by zero, lest thee bringeth a mighty tragedy unto thine land."

What a cop out, this isn't solving a math problem, he just thinks he is being clever, by using a "symbol". Wow, well I will redefine math too. 1/2 is nolonger 1/2 but !@. Recognize my skills!

Ummm... My last post hasn't shown up yet, but in case it does, I made a typo. 5/1 is 5 because 1 can go into 5 five times not 1 time. :-)

John Wallis
I came up with this in the 1600s, and I picked a better symbol!

I'm pretty sure my Maths teacher came up with something similar. Then again, he couldn't spell "bigger". Actually, he looks a bit like like THIS crazy dude.

my name is NEO
well given this i can make up results like 0 * infinity = nullity and 0*-infinity=nullity and keep on going... so nullity is still undefined, which is what I learnt in the first place. So whats new? the word??

Forget 1200 years, BILLIONS!
Why 1200 years? This has NEVER been solved until now. So, we should say 4.1 Billion years (perhaps longer...). Whoa. I can't wait until they integrate this theorem into airplane autopilots... and nuclear missle launch systems. We really need it there. "My game's like the Pythagorean Theorem. It ain't got no answer." - Shaquille O'Neal

Keith Braithwaite
Oh dear. The days are long gone when attempting to divide by 0 caused computers to "just stop working", and many programs that do numerical work already use a value called NaN (for Not a Number) to handle the results of such operations.

N/0 = UNDEFINED. He just renamed UNDEFINED = NULLITY. I see this as a publicity stunt rather than true mathematical news.

my problem is that I cannot except the zero exists at all

N/0 = UNDEFINED. He just renamed UNDEFINED = NULLITY. I see this as a publicity stunt rather than true mathematical news.

Nullity is already defined as a yang to a kernel’s ying. To say yang exists is to define ying as Nullity. So only in the {} this is true. As {} not equal {0} then the theory is false. Shame on you people for mixing apples and oranges for the ignorant.

I'm surprised at the comments that say something like this: There are 5 apples and 5 people. 5/5 is 1 because each person gets one apple. There are 5 apples and 1 person. 5/1 is 5 because each person gets 5 apples. Also, if there are no people, then 5 apples are left so 5/0 is 5. NO! You're assuming that something is happening to these apples if there is no people. It's called division for a reason. The old answer would say that it's impossible to define this scenario because "How can you divide 5 things among 0 people?" The new definition is this: 5/5 is 1 because 5 can go into 5 one time. 5/1 is 5 because 1 can go into 5 one time. How many times can 0 go into 5? More than 1? Yes. More than 5? Yes. More than 700 billion times? Yes. The answer is infinity. BTW, don't we already have a symbol for infinity? It's a bloody sideways 8!

Someone with an actual degree
Attention whore....sigh.

US Gringo
If it's a 1200 year old problem, then how did Pythagoras (b~ 570 BC) go over 1500 years into the future to try to solve it? Interesting read nonetheless...

1>0>-1, all are knowns ...-1<...0... all are known from a practical perspective. we have always had an application problem dealing with the unknowns. applied and theoretical math accept that there must work significant weight is fact existing unknown conjecture which do our best to cope. at macro level reasonably speculate hypothesize objective observational knowns. zero one time was not in mathematics ... i know what may be accepted this or next millennium but very big help maybe something identifier overlooking need define advance science math. anyway reasonable logical defined today does unknowns for tomorrow. ps god mythology>

He didn't solve anything. Now we have a symbol for nothing. Great. Good work.

Kate Meloney
Are you kidding me? It has no place on either the real-number line or the complex plane. What happens to Lim h-->0 (0/h)?? It's value is zero, but at h=o, suddenly it skips to some Nullity number? No...this doesn't work.

Dr. Anderson has done a really clever thing. The same pattern of discovery and progress was made when the symbol for zero was invented. So what he did was essentially the same: use a symbol for something counter-intuitive or previously unrepresented in calculations and formulas. Intelligent.

Robin P
It sounds do-able, but seeing as this is an older article and it still hasn't made headlines or changed the Calculus books around the world, I am thinking that it has been disproven, or at least, has too many flaws in it and needs to be more defined before it can be called a theorem.

Johnny Cash from beyond the grave
The idea is stupid, you can call dividing by zero whatever you want. His idea of 'nullity' is something mathematicians already understand and are constantly tackling with. His idea really is to let computers deal with dividing by zero. He hasn't answered any questions about dividing by zero.

This is just pure nonsense.. A problem that Newton and Pythagoras could not conquer..? Yeah, right.. The idea of introducing a symbol for the operation of dividing by zero is very old and simple. It is in no way revolutionary and has nothing to do with hard unsolved problems.

I want to believe Dr. Anderson is familiar with the classic comic routine where Lou Costello shows Bud Abbott that 7 * 13 is 28 via addition, multiplication, and division.

Hey, did you people know that 22/7 is a pretty good approximation to pi? Its pretty neat, I use it all the time when I program stuff in languages where I dont know how to call on pi. My simulations are off though, but it compiles :S. So do I get a price?

Matt Eustace
It is so incredibly easy to prove this idea wrong. In fact, the proving wrong of this is actually covered by the syllabus of A level further maths!

This is useless.

Silliness. Division by zero is 'impossible' because there are an infinite number of correct results, not because we were lacking some stupid new symbol to represent it. I challenge the professor to bring that to the entire educational community and see if he A) wins the Nobel, or B) gets laughed out of the building.

dan allford
this is definatley the stupidest thing i have ever heard. if this is what you call x/0 then it is still undefined.

So he just invented a number to solve the problem? How is that math? Why not call it X where X=0/0. It's nonsense. Besides, 0/0 = infinity.

It looks like the guy just came up with a symbol to represent the impossible equation of 0/0. This seems neither novel nor interesting.

For all we know: 1/0 == chicken. I agree with all those who have said that he has just renamed the solution - this is not a new idea.

Everything to the power of zero equals one! Everything divided by itself equals one. This guy has solved nothing at all. Just replace nullity with 'one' and it'd make even more sense.

alan r. math grad
I am very interested in reading Dr. Anderson's paper when published. But what strikes me most interesting is that there are so many extremely strong reactions against his idea. Obviously it has struck a chord with a lot of people and that often happens when a long standing idea is challenged. (At one point in time not too long ago it was just taken as fact that the sun revolved around the earth. Challenging that idea could have resulted in your execution.) Unless you have already read his mathematically rigorous theory and proof as would be published in a paper and found a rigorous flaw with it, i think it would be premature and immature to dismiss his idea or resort to name calling. Mathematicians should have no reason to feel threatened by his proposition if indeed it is "so obvious that he is wrong." But it appears that most of the comments are intended to do just so after only having read an article written in layman's terms. Number fields are defined by axioms - if he has been able to define a set of elements that adhere to the axioms, then would be nothing mathematically incorrect with his arguments. I have not seen anywhere where he has stated that nullity lies in the Real Number field; thus it does not "break" the arithmetic of numbers most people are familiar with. He is in fact saying that nullity "sits outside the conventional number line." The problem is that it may be very difficult (albeit not impossible) for the average person to come up with a metaphor to help them understand nullity. For example, you don't have to understand the Rational Number field to know that 1 apple plus 1 and a half apples is 2 and a half apples. People often use this lack of understanding to give themselves permission to use the perverse justification: "If I don't understand it, it must be wrong/he must be an idiot." Dr. Anderson has an interesting idea and once formally defined then it should be reviewed critically.

Oh great next time check something like this with someone who is certified in maths by a university. I mean this is nothing else then what the IEEE defined as NaN (Not A Number) for computers. The reason for calling it not a number is because it can be litterally any number and it is unknowable which number. Thus anything that would be unsolvable prior to inventing nullity would still be unsolvable due to the inability in translating any result that uses nullity to a number because you have to translate this solution to every number.

Bigger problem
WoW! So we found out how to divide by zero now we have another problem. How Do we Divide by Nullity. Do you see were this is going?

"nullity/nullity = 1"?!?!? Ofcoz NOT! X + nothing = X X - nothing = X X * nothing = nothing X / nothing = nothing nothing / nothing = nothing There must no be terms like "negative nothing". "Nothing" cannot be negative or positive because it's just nothing. Actually... I hate mathematics and theoretical physics. Because of stupidity. These "sciences" full of artificial crap. Yes, some artificial constants can work for known(!) problems. But who said what we know everything? We are dust in the Universe!

Jason Jacobs
for a computational system to be 'universal' we must be able compute the answer 'undefined'.. if all answers are definable then the computational system is not 'universal'.. this nut job has 0 understanding of computation. He should read turings papers on computational universality..

Oh Dear
The comments above say it all. BBC, shame on you. You are truly an embarrassment.

Dr Anderson's concept is ideal for people who suck at calculus. Nullity does not solve problems, just avoids them. When solving a calculus problem, reaching 0/0 forces you to find the PROPER solution for the problem, using a number of theorems developed throughout the centuries, those actually designed to SOLVE the problems at hand. Lazy programmer.

Kristopher Kirkland
1) Before bashing this man's intelligence or his theory, please actually read his work, rather than what boils down to drivel and a photo op (you wouldn't trust the local newspaper to perfectly explain Einstein's Theory of Special Relativity). 2) Most program are engineered not to encounter a division by zero, however if one occurs, an exception will occur, an depending on the machine, it may crash. 3) All your proofs of how his theorem say infinity=0 boil down to using something like 1/0 * 0 = 0, however this could be rearrange to 0/0 * 1 which equals -0-. 4) NaN and indeterminants are not solutions to the problem of 0/0, they are work arounds. Ways of avoiding dealing with the 0/0.

Wow, so now my pacemaker's going to crash with an 'unexpected null value' bug instead of a divide-by-zero bug! Revolutionary stuff eh.

Cool, so can I publish my theory about 7 being the last digit in pie? Don't belive me...disprove it :P

Maplesoft (creators of Maple) solved this problem a long time ago, they use the word Undefined. Or the word infinity if the limit actually approaches the same infinity from both sides. I have no idea what this guy thinks he is doing, but it doesn't accomplish anything. When you divide by 0, you have two choices. If the division by 0 is done by having a simple polynomial approach 0, you can take the limit and work with that. However, if the limit is undefined your computer program has to give some sort of error otherwise all results after that point will be guaranteed to be wrong. This is simply from the fact that in a structure which repeated calculates something, if I hit a point where my variables are undefined, I am screwed. I need to throw an error and then try to use some other method to determine a way to redefine my variables again. This is especially important if I am dealing with a real-world scenario like medical equipment. In Maple, they use a term called undef, which basically has the property that any arithmetical operation done to undef remains undef. Which is completely and totally useless, because (if this was a medical computer, for example) that does not tell me if my patient is still alive or not, or how much medication to apply to him. It also does not tell the programmer whether or not they need to catch the error and deal with it. So basically, this nullity is either a new word for undefined/infinity or something even more useless (and dangerous if used). BBC should be ashamed for publishing this tripe.

So essentially we're taking the set of things that are undefined and calling it "nullity." This is new and amazing how?

It appears he's just taken an element of Calculus (lim x->0-) and come up with a new name and symbol for it for use in algebra. And it has no real use for computers; it'll only result in a software catch to make sure that when 0 occurs in a divisor, a different logic path is taken. And we've been doing this anyways.

Brian Matthews
I find it very worrying that this is being presented to schoolchildren as fact. There is enough mathematical illiteracy without this mountebank adding to the problem.

Armend Ademi
If I have 10 oranges and will share them with 1 person(10/2=5)I will get 5 oranges. But if I don't have no one to share oranges with (10/0=10)than I will get all of them, 10. In that case I see 0 like 1:)

some american
Hey, I've got a proof that holds just as much weight. ... = 0/0 = 5 Therefore, division by zero equals five. Tell your friends.

Wow, personally i am impressed. I should have scribbled on a paper and submitted it to BBC years ago with an = 0*0 next to it.

anonymous coward
this story is of singularly (no pun intended) stupid quality. mathematicians have, since at least riemann, had no trouble dividing by zero when it was needed and in some legitimate. in fact, introducing a symbol for 1/0 is usually referred to as adding a point at infinity (for obvious reasons) and is a technique introduced to undergradutes. this is not news.

Simon Hastings
I don't know if this has been commented to(since there are alot of them), but the reason deviding by zero is undefined is not because we can't find a definition for the results, but because we can find TOO MANY definitions. Take A/A, where A equals zero on the top and bottom. Now limit them as A goes to zero - the result seems to be 1! Likewise -A/A seems to produce -1. Seems Fair. What about 1/0 from the left - whoops, negative infinity, and 1/0 from the right gets us positive infinite, and 0/A from any direction gets us Zero. So what do we make it for all cases? No idea. Thats the real issue.

Eric Towers
The arguments of the form, "He just made up a new number. Bah! How useless!" are amusing in the context of mathematical history. Similar comments were made for negative numbers, irrational numbers, complex numbers, transcendental numbers, et al. Much growth in mathematics has come from taking a step back and accepting more things as numbers (and making up symbology to label the new numbers). So this form of knee-jerk reaction is pretty funny. I am concerned about Dr. Anderson's displayed proof. The production (0/1)^-1 --> (1/0)^1 is on shaky ground (without more explanation) since it requires a theory of division and division is the operation that is being modified in this extension. Also, the claim that the set of axioms with the nullity axiom(s) added is consistent is probably weaker than stated in these comments. At best, the statement could be "arithmetic + nullity is as consistent as arithmetic". Godel has convincingly argued that we will never prove the consistency of arithmetic or any system that contains (i.e. can represent) arithmetic. So, the highest attainable form of consistency for such a theory is "at least as consistent as arithmetic". Regarding the question of "division by nullity", application of the axiom gives (for all x (including the three new symbols), and using "O" for nullity): (x/O) = (x)^1(O)-1 = (x)^1(O)^1 (because (0/0)^-1 = (0/0) by the syntactic transformation (a/b)^-1 -> (b/a)^1 ) but this is (x*0)/0 = 0/0 = O. Explicitly (re-)checking the new symbols, only the step x*0 is interesting: (1/0)*(0) = (1*0)/0 = 0/0 (-1/0)*(0) = 0/0, similarly (0/0)*(0) = (0*0)/0 = 0/0 So the proposed extension seems to provide closure under division. I'm concerned that (2/0), (3/0) et c. nonstandard numbers are not defined. This worries me because this extension looks a little like nonstandard analysis of infinitesimals "inside out". I.e., where the dualities (nonstandard infinitesimals

Quite stupid. This introduces NONE of a concept, just a new symbol that means nothing.

I think this is just great

This is the same thing that everyone has said but here goes anyway. This theory has been around for a long time. It reminds me of the theory of imaginary numbers. The problem is unsolvable, so a number is made up that solves it. A NAN number. you can't define infinity as 1/0 because infinite has no definition other than that it is endless. This argument is just like the people who argue over how close a googol-plex-plex is to infinity. A googol-plex-plex is the same distance from infinity as 1 is, because infinity is endless, it has no exact value. I'm sorry Dr. Anderson, but you just got OWNED!!!!!!!!!!!!!!!
One would hope that auto-pilot and or pacemakers have their calculations set to workaround the "divide by 0" catastrophe noted by this teacher(?).

This is a very old idea that has been part of computer science and electronics for many decades. Computer Sceince has had the value NULL for over 20 years. Electronic equipment has had tri-state boolean values 1,0,OFF for even longer.

This makes me ashamed to say I come from Reading. :'(

Realplayer has just crashed on me with a divide by zero error! How?????

Exactly how much does this university pay this guy to clearly do nothing all day? "Imagine you're landing on an aeroplane and the automatic pilot's working," he suggests. "If it divides by zero and the computer stops working - you're in big trouble. If your heart pacemaker divides by zero, you're dead." So you check first to make sure you're not dividing by zero. And then what? The autopilot says, "nullity." Your pacemaker says, "nullity." Yer dead anyways!

I wish my high school math teachers had been this open-minded. Making up solutions on the fly would have seriously helped me in Calculus.

Tom Ritchford
Um, you perhaps need some editors with a better grasp of mathematics and its history. The specific idea of enhancing the number line with a positive and negative infinity is well over a century old and was neatly formalized as part of Abraham Robinson's theory of infinitesimals half a century ago. This isn't particularly obscure stuff -- first year University students have been taught calculus using this method. The "nullity" idea appears to be just plain wrong. You can certainly add any symbol you like to represent 0/0 (though phi is a poor choice as it already is used to represent the Golden Ratio). Unfortunately, you can't give this new "nullity" number any sort of consistent behaviour when you add, subtract, multiply or divide by it -- it's more like a symbol meaning "put down your pencil now". Mathematics has also had this exact idea for centuries now -- the result of this calculation is "undefined". This is what I was taught in primary school many years ago. For Dr. Anderson to claim that he has solved a problem that has lingered for 1200 years is hubris, plain and simple.

I tried to convince a teacher in HS that 4.pi was a number... she didnt buy it. Maybe this guy can come up with a theory for it to help me out!

Zero divided by zero = nullity? WTF? 0/0 = 1 1/0 = 1u 2/0 = 2u 2u*0 = 2 That makes a lot more sense.

What is Nullity/Nullity ? What is Nullity X Nullity ? What is Nullity^Nullity ? What is 0^Nullity ?

Vic Snowden
I can finally sleep!

Can you not say "20 divide by zero equals zero remainder 20"? That makes more sense to me.

Ewen Malloch
So 0/0 is nullity which can be drawn as a point above or below (or left or right presumably) of the number line. Geometrically, this implies it has a length - a distance from 0, similarly to i having a length of 1. So there must exist a value twice as long or twice as far from 0, so 2*nullity (compare with 2i). 2i can be represented as the square root of -4. What can 2*nullity be represented as in terms of the number line? Is it still 0/0? If so, surely you've defined a singularity as all points expressed in terms of "nullity" can be represented as 0/0. The references to getting "errors" when computers divide by zero is just poor programming. Yes, it produces an error by the code should resolve that error cleanly - by defining it and an action to take. How is that different to a definition of nullity or NaN?

All you people that discredit this are just jealous fools who wished you thought it up first. So go back to your hole and sit down and shut up.

So, will the IRS allow me to submit a nullity return?


Content Free
You have failed to show how assigning a symbol to positive and negative infinity changes anything, other than the student's ability to write the symbol in place of "undefined".

Another silly theory: 0/1*1/0(As above) =1/infinity*infinity =1 ohh which is what all other numbers are to the power of 0. Therefore according to the above 0/0=1 so nullity=1 therefore according to this you have reinvented 1

Beautiful ! Congratulations ! The numbers of variations of an innumerable set of problems might now work out to become practically possibilites for anything from physics to mechanics. A great great breakthrough - If I had a say I would call it Nobelprize-worthy !

What's Pi in binary?

Bravo to Dr. James Anderson. Your work is simply excellent, even if these self-professed by opinion "experts" can't comprehend the consequences of your important discovery. I will be following your work further.

Felix Persson
Did Pythagoras live 1200 years ago?

Suprised Swiss Computer Scientist
Ahem ... I _think, 0 to the power of 0 is 1, and not Nullity (whatever that's supposed to be). This whole thing is ridiculous and there could only be one day in the year where I would understand this appearing on the BBC web site, which is April 1.

George Cook
Read chuck norris's ninja comment. Thanks chuck - elegant and insightful - this "professor" would be much better teaching his calss your way. Also - I hope that the year 13 stats comment was not someone in his class.!?

Real simple
so, nullity? ok, on a real computer, if you wanted to prove nullity (or non-trueness), call it NULL or NIL. x / 0 = NIL there is your nullity right there. wha does it solve? nothing, since nullity is itself undefined.

Don Philip
The mechanics of the theory itself are easy enough to understand as far as he has presented it. However, locating a number off the number line is the problem, and to fully understand what he has done, one would need to understand the mathematical justification for being able to do so. Otherwise it's a little like saying that you've come up with a new number (we'll call it snark) that equals the square root of negative 1. Without a proper justification or proof, it's just a word with no meaning. Dr. Anderson needs to make his proof more clear before I can accept this.

Forrest Gump
Mama always said... Nullity is as nullity does...

This has to be a joke.

A Random Smart person
Dear sir, trying to get your name in the history books by saying nothing is nothing will not work. You create this highly obstrusted math to try to show something that is to be something it isn't. N/0 = undef for good reason. Trying to say 1/1 = 555555/555555 its true but it isn't so. Good day.

APRIL FOOLS! - Oh wait, its December.

Tom Horseonovich Colligan
I have followed this thread with interest, and agree that perhaps the best forum for exploration of a new theorem is not in a classroom of young students, but before a curious and critical group of advanced mathematicians. Though there are issues with this new theorem which appear to render it false when examined in a purely mathematical context, I do see value in exploring the possibilities of "nullity" within the realm of computer science. Tom Horseonovich Colligan Rouse Ball Professor of Mathematics Cambridge University

Alex Zavatone
I don't understand it because I can't see the video. Please use some cross platform video file format like .mp4 so more people can view the video

norwegian guy
This is an old "solution" to the problem, it has just not been accepted as a solution. Imaginary numbers (numbers which sits outside the conventional number line )has been used for hundred of years in calculating negative square roots and equations that have no solutions. But its still not a good solution to a problem, as the calculation is not possible using "accepted" mathematical methods.

alan r. - math grad
I am very interested in reading Dr. Anderson's paper when published. But what strikes me most interesting is that there are so many extremely strong reactions against his idea. Obviously it has struck a chord with a lot of people and that often happens when a long standing idea is challenged. (At one point in time not too long ago it was just taken as fact that the sun revolved around the earth. Challenging that idea could have resulted in your execution.) Unless you have already read his mathematically rigorous theory and proof as would be published in a paper and found a rigorous flaw with it, i think it would be premature and immature to dismiss his idea or resort to name calling. Mathematicians should have no reason to feel threatened by his proposition if indeed it is "so obvious that he is wrong." But it appears that most of the comments are intended to do just so after only having read an article written in layman's terms. Number fields are defined by axioms - if he has been able to define a set of elements that adhere to the axioms, then would be nothing mathematically incorrect with his arguments. I have not seen anywhere where he has stated that nullity lies in the Real Number field; thus it does not "break" the arithmetic of numbers most people are familiar with. He is in fact saying that nullity "sits outside the conventional number line." The problem is that it may be very difficult (albeit not impossible) for the average person to come up with a metaphor to help them understand nullity. For example, you don't have to understand the Rational Number field to know that 1 apple plus 1 and a half apples is 2 and a half apples. People often use this lack of understanding to give themselves permission to use the perverse justification: "If I don't understand it, it must be wrong/he must be an idiot." Dr. Anderson has an interesting idea and once formally defined then it should be reviewed critically.

A. Caranti
I read one of the two papers Dr Anderson co-wrote, and it seems to me that once you get Phi (the "nullity") in an intermediate step of a calculation, you are stuck with it for the rest of the calculation, in the sense that every operation that involves Phi will always give Phi as an answer. So what would you like better, a computer that works for an hour, and then gives you Phi for an answer, or one that after a minute or so tells you "Look, Doc, you just asked me to calculate 0/0: you want me to keep working for an hour, and then give you Phi as an answer, or perhaps you prefer to reconsider the programme you asked me to run?"

Seiko Flossberg
Good idea, because it happens all the time that pacemakers divide by zero and stop working. In case you didn't notice, I was being sarcastic.

If Dr Anderson's axioms are consistent, and more importantly as far as mathematics is concerned, novel, then he deserves congratulations. I don't see any use for them currently, but that doesn't mean there isn't one! Other extensions to the excepted set of numbers were also thought to be useless at the time (I'm thinking of imaginary numbers), but became hugely useful later.

Are you actually saying division by 0 is possible? Because writing 0/0 presupposes that division by zero is possible. If so, consider the following: 1*0 = 0, so 0/0 = 1 2*0 = 0, so 0/0 = 2 3*0 = 0, so 0/0 = 3 etc. If division by zero i So does "nullity" = any number I want it to equal?

Division is just a short-cut for subtraction; any problem becomes: 'How many times can you subtract x from y?' An the answer to how many times can you take nothing from something? Is infinity.

Ranjit Wassan
Underwhelming story... Why doesn't the BBC cover zero point energy sources such as Stan Mayer's Water Fuel Cell or the Folks in Australia that are driving around their cars running on water. Modern Science is stuffy ans arrogant. If it work then use it. Maybe the world would be a better place if we did not have to rely on Oil! BBC - Bring us HHO gas stories!!

Rick Spivill
Another triumph from the University of Reading's comp sci dept.

Mahesh Sooriarachchi
I think this is just re-naming the problem to something else... then again, if you really think about the basics of division, the problem of division by zero comes into being because of the idea that zero is not really zero, but a really, really small number. So maybe the solution this problem should be to define zero as being trually zero (ZERO), nothing, zilch, nada! Now if you look at division this way, lets say you have an apple (thinking of Newton) to be divided among 2 people... each gets half. Now if you divide the apple between ZERO people, what do you get? I beleive its the whole apple... so dividing by true zero is the number itself!

Jon Baker
Proving that NULL exists and giving a cutesy name. Now why did I not waste my time doing that??

I was wondering... what would be the result of nullity/nullity ?

Kurt Fitzner
The "problem" of a computer with divide-by-zero errors is not a problem, it's a feature. It's not something you need to or even want to fix. You could easily design a computer that doesn't have an error in that situation if that's what you want. Replacing the error condition with a new symbol accomplishes nothing. The program still has to deal with the issue in order to present a real-world result to the user. A divide-by-zero error is the way programs do that. It's easy to solve a "problem" when you're the architect of the definition of the problem in the first case. Dr. Anderson first defines a problem: calculators and computers throw an error when you try to divice by zero, and then defines an artificial solution - but the problem was artificial in the first place. We've all run into poorly designed programs that don't handle divide-by-zero errors properly and crash. This isn't a problem of dividing by zero, this is a problem of a computer program not handling its data properly. We've also all run into programs that attempt to reference a null pointer. By the same reasoning, we could define the memory that a "null pointer" points to as some new type of virtual space called "nullspace" (trekies should appreciate my resistance to the temptation to call it "subspace"), and call it valid. Make the computer such that reading from "nullspace" always returns a null. Suddenly no programs crash from dereferencing a null pointer any more. It doesn't mean that the program is going to now do something useful. It probably means it will end up displaying garbage to the user, hanging in an infinite loop, or branching off to never never land. As far as it goes mathematically, there's nothing you can do with nullity on paper that you can't do by simply leaving it as (0/0) in the equation. So from either approach (mathematically or from a computer science perspective), it's nonsense. The author's own response to some of the critics (or, I should say, alleged response) doesn't help my opinion. Tossing out the names of two other Ph.Ds and offering vague references to undescribed "axioms" built around this new symbol all reinforce my opinion that Doctor Anderson sounds precisely like the character Robert from the movie "Proof".

He's worked his way in an apparantly conventional manner to where 0/0 = 0^0 Okay. Then he assigns "nullity" to both sides. So what ?

So wait, let me see if I understand here. Nullity = 0/0. As the professor showed us, 0=1+(-1). So 0/0 = (1+(-1))/0 = (1/0)+(-1/0) = Infinity + Negative Infinity. As everyone knows, anything minus itself equals 0. So this means Nullity = 0. Do I win a prize?

So Dr Anderson replies saying he IS using 1/0 = infinity which is false (1/x tends to infinity as x tends to 0, but this does not mean 1/0 = infinity) If he defines Nullity = 0/0 and Nullity does not help with x/0 problems on computers (testing for division by zero is already done and testing for nullity is as easy) then what use is it ... this does not explain that and neither does his reply on this forum This might be relevant and useful but not to computer science - computers already cope quite well enough ... but what does it allow you to do? this has not been explained?

i just read anderson's post. he seems to be using the real projective line and then saying 0/0 is not on the real projective line. and this gets published as original?

If a computer program divides by zero and crashes, that is not the computer's fault, it's the programmer's fault. It's throwing an exception, and if you don't catch the exception, then you're not a very good programmer. This PhD didn't listen very well in his first year CS course.

fellow anon
wow, anon really left alot of messages tearing this guy apart. i wanted to respond to some below comments, but there is no >>1748433373 to click on. However this is /0 GET.

This is totally amazing I love you man =)

Darren McDonald
This is nonsense, nothing has been solved. Your average maths A-Level student would be able see that. The BBC should feel ashamed for publishing this.

if "Let me try to answer..." is really by that "Dr James Anderson", I just can't understand he can teach somewhere. The only thing I like here is the "General Error has occurred" message (Dr Anderson's theory in detail).

I hate to add to the slew of comments, but I can't stop myself. You can't do this to the real line and preserve it's properties. At the fundamental topological level, positive infinity and negative infinity aren't on the standard number line - it doesn't have upper or lower bounds. And if you tack on another point "outside" of it, you change the topology. Is that point an open set? Closed? 0/0 isn't a problem that can be "fixed". It's a property of the real line.

Hmmm ...: Inf = 1 / 0 Inf * 0 = 1 [A] Inf * 0 = (1 / 0) * 0 Inf * 0 = (1 / 0) * (0 / 1) Inf * 0 = 0 / 0 Inf * 0 = Nlty [B] By [A] and [B]: Nlty = 1

Nullity is merely a symbol that says "I don't know". Not quite as groundbreaking as it's being made out...

My god that does it P=NP ... it's finally proven.

Nullity may solve the problem of writing 0/0 as 0/0, but doesn't solve the general problem of dividing by zero. What we need is a new sign, not a new number. Look at it this way, if you divide 23 by 0 and get nullity, try multiplying nullity by zero. Do you get 23 back? No! What do you get back? Another nullity? Zero? Where's my 23? Now consider a new sign: '@'. 23/0=@23 -23/0=-@23 @23*0=23 -@23*0=-23 Start looking in the second dimension and see the number line is not ---, it's -|-

Dr of what?
Simple proof that breaks "nullity": y = y y2 = y*y (y-y)(y+y) = y(y-y) &#934;(y+y) = &#934;y [divide by zero] &#934;y + &#934;y = &#934;y 2(&#934;y) = &#934;y 2=1... ?

Mark Skerritt
If you have 0/0, its undefined, use calculus to get the desired result. This is useless.

I don't know where you guys have been all these years, but math did not just drop into our laps fully formed. It's always been about defining systems that are governed by rules (axioms). As long as your system is internally consistent it is valid. (There are non-Euclidean geometries where triangles can be made from three 90° angles.) Now some consistent systems are more useful than others; if it is true that Dr. Anderson's system contains the whole of standard arithmetic along with this new definition, then I see no problem with it. I would be interested in seeing all of the axioms defined. Remember that for a long time everyone thought 1/0 was impossible to define, but now it is accepted that 1/0 = infinity. This new concept is really not much of a stretch beyond that.

let me guess, next someone is going to come out with an 'everything number', if it doesnt exist already, that contains every number [read:every state]. Schroeder's Cat = 'everything'

...really....? step 1. people don't know the answer to a problem step 2. ill name the problem "nullity" step 3. the answer to the problem is "nullity" wow I'm smart.

Martin Spamer
I'm a Computer Scientist not a Mathematician and a natural sceptic. However this is interesting because of the symmetry with how null IS handled in Software Enginnering. Null != 0 and is held outside the scale of real numbers. Null is usually represented as \0 which might present a better alternative than a new symbol.

All he's done is make a name for a problem to mask the problem... I don't think it really solves anything.

Kirill A. Woroshilov
And what does that guy think about L'Hospital's Rule?

Emmanuel D.
I am very sceptical about such "theory". First, it is quite confusing, and I don't see how it can help to understand some problem. if 1*nullity = 2*nullity, then nullity/nullity = 1/2 AND nullity/nullity = 2/1. But even worse, 1 = 2*nullity/nullity. So you have to say that nullity/nullity is undefined to explain this answer. Your transreal arithmetic fails to do this, as far as I understood it. Second, since it's still confusing, Iit would have been better to wait for for mathematical evidence before teaching this strange things to pupils. This is nearly criminal. Next year some other teacher will come with a theory that says that 2+2 can be equal to 5 for very large values of 2 and small values of 5. Will he be right to teach this to pupils before being confronted to his collegues? I think no. Working in this way is just plain dangerous. Science and math needs to be proven before they are taught - that's a basic fact. You also failed to do this, and this is criminal imho. Finally, nullity doesn't really help when it comes to computers. How will you represent it (and both infinity and negative infinity) using a 32 bits integer? Or a 64 bit integer for that matter? Remember you still have to follow the rules of 2-complement arithmetic... That's going to be quite hard. I guess the solution is to give them some special values, and to hardwire the calculus in the ALU - this is not very efficient imo. I don't want to say that the theory is some random bullshit (I'm inclined to think that a representation of these numbers is quite important), but I'd wait for better proofs - ie not proofs that are backed up with the IEEE FP standard.

Im no mathmatician (infact i struggle to spell it). So im not really sure about all this 0 stuff. But i think the reason math exists is to work things out, probably starting at some local shop and adding beads or something trade one loaf for two fo these or what ever. So in my ignorance I look at it simply, such as: Say we have One cake. We have 5 people. The cake weight 500g. So each person (if divided equally) gets 100g of cake each. So, if theres 1 person, they get the whole cake, 500g. So, if there arent any people to divide the cake between, doesn't that mean that 500g is still left? Crude, Im sure. But, surely thats right? 500/0 = 500? I guess this might be part of the problem, in maths this just cant work. I do find that there seems to be a few holes in the hole mathematical system and we seem hell bent on trying to keep it as the RIGHT way to do things. Its takes someone to try and prove other systems, it seems in todays world we appear happy to use old(ish, perhaps, although improved over time) methods that yes, have been tried and tested, but may be not entirely correct. If a tree falls in a wood and no ones heres it, does it make a sound. Yes, of course it does, dont ask such daft questions ;)

There is absolutely no need for this imaginary value. First off, any number to the power of zero is one. Why? Let's say N is a number, and R is some random number. RxN^0 is interpreted as, "Multiply R by N zero times," or more generally, "Multiply R by... wait, no, nevermind, just leave R alone." Next, let's address the concept of 0/0, or zero divided by itself. The simplest answer is that any number divided by itself is one. Obviously computers have a problem with this concept, so let's approach it from a more versatile standpoint. Computers have difficulty dividing by zero, because 1/0 is infinite, and computers only deal with finite numbers. That's the problem designers would need to fix. Instead of treating numbers as finite values, tack on an infinity tracker. Let's use oo to represent infinity, since I'm writing in a text box. The basic problem is that 1/0 = oo. In finite mathematics, that causes an error. However, 1 in a finite system is actually 1 not multiplied by any infinites (or not divided by zero). We could say that finite 1 is 1 multiplied by no infinites, or "one with zero infinites" as a shorthand version. Now divide it by zero. The result is one with one infinite. Now divide 1 by this result, and you get 1 (from 1/1=1) with -1 infinites (1/oo). Divide this number by zero, or multiply it by oo, and you're back to 1 with 0 infinites, or finite 1. To divide by zero at any time implies that zero is, in fact, not an absolute value, but simply an infinitesimal value; it is so small that it is regarded as nothing. This, from the perspective above, would be called, "one with negative one infinites." We could, of course, multiply it by itself to get the value, "one with negative two infinites." Multiply this by oo, or one with one infinite, and you're back to one with negative one infinites. Multiply by oo again, and you're at one with no infinites, or finite 1. Taking the concept a step further, consider the simple equation (x^2)-(2x)+1=(y^2). In finite math, that's a simple problem to resolve. What about if x = oo? The answer is that it's still the exact same problem. The answer, y=x-1, still applies. Writing out the equations, we'd have one with two infinites minus two with one infinite plus one with zero infinites equals the square of "y", resolving to "y" equals 1 with one infinite minus 1 with no infinites. So what's oo^oo? Guess you'd need to tack on a second infinity counter to the number at that point. While I wouldn't expect a simple hand calculator to handle this problem, any scientific calculator designed to handle the square root of negative one should be able to handle infinites in this manner. Getting back to the whole issue of "nullity", it's basically useless. Nullity basically means, "One multiplied by some finite numbers I was too distracted to track." If accepted by the mathematical community, it could easily be used to prove that 1=2, or a variety of other nonsense. [Gyeh. There are too many replies to this discussion already. Forgive me if someone has already said what I just said. It always seemed to me like a fairly obvious solution.]

I'm studying in the Reading University Mathematics department. I would like to point out that this guy is not a mathematician and works in the computer science department. Hence any theories that he proposes are nothing to do with the mathematics department.

David Mellor
Why such skepticism? I'll bet people would have said the same about the square root of minus one, and look how useful that is now (really!).

... Quite strange. If you are dividing something by 4 it means "divide in 4 pieces", isn't it? Ok. What is result of "dividing in 0 pieces"? Just nothing. What's wrong with it?

Inventing a new term to deal with it, is not really solving it, is it?

Try a different symbol, sir! That one your using equals 1.618 and it's one of my favourite numbers!

My understanding of the real numbers is that they don't actually end. So how can infinity have a value? That would mean the end of the real numbers, which is not possible.

I have nothing to say.

Albert Einstein
What is nullity divided by nullity? Negative infinullity?

If this problem hasn't been solved for 1200 years, who solved it 1200 years ago?

If the definition of infinity (positive) is 1/0 then is 2/0 not two times infinity? This would be a larger infinity by the math rules that I know. This concept can be extracted an infinitum. As a result, 1/0(1/0) is an infinite infinity, also know as an absurdity. Does this make any sense? Infinity is infinite by definition and therefore nothing is larger. Maybe, just maybe Mr. Anderson is 1/0 nuts. That's it, the man is off his blinking rocker. Now for there real issues of life - just how many angels can fit on the head of a pin?

1. if you read his axioms you will realise that "nullity" is what humans have been calling "undefined" for 1200 years. The axioms are identical. He just renamed the word. 2. if your heart pacemaker divides by zero you are NOT dead. there are things called watchdog timers that reset microcontrollers when things like that happen. 3. creating an object out of "undefined", called "nullity", that behaves identically to what we have always known as "undefined", does not help computers or mathematics any.

Dr James Anderson wrote: "It is just an arithmetical fact that 1/0 is the biggest number there is. " Rubbish. That's about as meaningful as saying that an orange divided by an apple is a pear. 1 is a quantity. 0 is the lack of a quantity. Using symbols from the same numerical system for both of them creates the intellectual illusion that they are both numbers, but they are not. Thus, the entire nullity edifice collapses upon itself.

Beender Dundat
My theorem: any number (includig zero) devided by itself is 1, ex. 1/1=1, 123/123=1 and 0/0 = 1 and infinity/infinity = 1. Also, any number (including zero) to the power of 0 is 1. Anything devided by zero is infinity (positive or negative, depending on its sign). Clean and simple.

Ehhmm... Thats strange - To declare a new "number"/"letter". I'm not happy about this solution. I'm sorry.

Hi, If this problem is 1200 year old, then what does Pythagoras have to do with it?? And as physicist I did not see any new math here.

Any Java programmer will be able to see the similarity to Double.NaN (Not a Number) constant. This was introduced by Sun atleast in 1996, could have been earlier if done in other programming languages too. The only extension here seems to be that its being brought into the non-programmer world.

Brian Matthews
Here's why 'nullity' doesn't work: WHat is nullity divided by nullity? Well, it's 1, isn't it? On the other hand, this is also equal to (0/0)/(0/0), which by simple maipulation of fractions is equal to 0/0, which is nullity. So nullity equal 1. Nonsense. QED.

Guys, this story is in no way analogous to complex numbers. Complex numbers are no more or less artifical than the negative integers or rational numbers, they're all just extensions to provide a superset. They are in no way like what is being suggested here, which by the way, is an embaressing regurgitation of absolutely nothing. Ignore all research papers from the University of Reading.

Navid Zamani
I KNEW it! I KNEW it the WHOLE TIME! Never since i first heard that there is an "exception" to all math, when using zero, i felt very strong that this is wrong. Like a glitch in the matrix or 2+2=5... You know it. I searched for solutions to it. But they mostly went with "something / zero = infinity_n" where n held the information about "something", so by muliplicating "infinity_n * zero" you would get "something" back. Worked quite well, but there were problems with it.... (that i can't remember for now) I'm REALLY happy this happened! So i finally can tell my ex-teachers that *I* were right all the time! THANK YOU MR.... Anderson...? Oh... my.... GOD... I's you Neo! You solved the glitches! :D

So, how does this relate to the theory of algebraic wheels; which as I remember it also deal with 0/0 by extending the extended reals to include this as a new formal element?

Three High School Math Teachers Mr. Gagliardo, Mr.
This is not something new under the sun. 0/0 is undefined; but it can be also be considered indeterminant because it can be any value. 0/0 could, for example, be 7 because 7 x 0 = 0. It could also be -41, .2, etc. Calling it nullity is just a bit too cute. However it gave us something to think about.

Kyle Burton
I'm sorry, but there isn't exception handling in integer division

Funny That
This has to be a joke of some sort! Some great comments below though: Bob:"The program wont crash, but the plane sure as hell will." :0)

Dr Richard Daniel Hill
This man is a charlatan and a crank

0/0 = Nullity? Next thing we know, he will tell us that .9~ =/= 1.

nullity.complex: defn: people with nothing to do b
It does amaze me that so many smart people feel the need to shoot down another mans ideas....whether bad or good. Obviously little else to do with their null lives. Its easy to be a critic. And nearly every commentator has come up with the solution at some stage in their young lives. One things missing...why did these people do nothing with their new ideas? Even great minds had solved problems in the past, but gained no recognition for it because one has to see opportunity/value in such solutions. From my point of view: if i take 10/5 = 2 and convert it to 5*2 = 10 then I would expect that 1/0 = ? could be rewritten as 0*? = 1 but multiply by 0 gives you 0. This is what we've always been thought. We can also never tell if 1/0 is negative infinity or positive infinity yet both are possible. NULL is used in computer programming to define mean nothing/empty/undefined. Its allows checking for the existence of something of interest. Comes from the latin word nullus meaning "not any" Is it not possible the professor is trying to explain this theory through algebra..... I cannot view the video so I do not know. And so what if its been discovered. I'm sure its a helpful approach to teaching this stuff.

I wonder how Dr. Anderson handles (a real number)+(infinity) - (another number)-(infinity). Since his infinity lies where it does, how does he handle it?

if: 0/0 = Ø so: 0/Ø = 0 then: Ø = 1 ??? nullity = unity ???

Adam Braun
Express it as binary.

Every field has a nullity. That's basic abstract algebra. One should be wary of people defining things conveniently without rationale or proof - what you've got there is just numerical masturbation. Avoid mathematical sensationalism at all costs!

I came up with the same solution years ago except I used the symbol "Doh!".

Thom Howes
Simple question, if the numerator and the denominator both approached 0 at the same rate, wouldn't the result always be 1?

It's true that dividing by zero does cause an error in programing, but any programer that has every written a program more complex than "Hello World" (Tradtionally the first program you ever write), will know to trap the error before it occurs. So it can be dealt with gracfully (i.e. assigning a defaul value instead), rather than crashing. Any of the modern or Object orientated programing language will have expection handling built into the it for just this sort of problem. As a computer scientist, I would have hoped Dr Anderson would know better.

Mutant Rob
So has he vetted this idea in reputable maths journals among other mathematicians, or is he using his power as a school teacher to foist quack ideas on his students, much like "rational trigonometry"?

Newton? Fool. Pythagoras? Useless. Anderson? God. Eat your heart out, creators of mathematics as we know it!

The Mole
So: Ships and planes unexplainedly disappear in the Atlantic. Let's assume there's a location which lies outside the normal space/time line and give it a name. Now the disappearances are all explained just by saying "Bermuda Triangle".

It's been a long time since my Advanced Theory classes, but doesn't a number lying OFF the number line violate the axiom of Completeness? I find it hard to believe Dr Anderson would have simply overlooked the most basic axiom in advanced mathematics, but that's exactly what he appears to be doing. Before contradicting the use of the term number here, let's face it, anything used to represent a value is a number, even if you call it a non-number. I have a problem wrapping my brain around a value divided by a value producing a non-value. One might as well say 6+10 = a dog. This is violating - or rewriting if you prefer - a number of concepts that the vast majority of mathematics, from simple computation to advanced theory - relies on. I won't go so far as to use the derogatory terms presented by other commenters, but I certainly think dropping this from the drawing board to a schoolroom without peer review and general acceptance is irresponsible at the least. I do realize that the particular problem of division by zero is a particularly anomalous one, so I can understand the unorthodox approach, but there are times when either infinity, negative infinity, zero, or 1 tend to "fit" human intuition - which we all know is not always even close, but for real! I do think there's a way to handle this, but I think it's maybe just a little more involved than "Hey! Let's make up a new (non)number!"

Anyone know of a credit card with this kind of interest rate??

No body
Take the pairs (a,b) of real numbers. Two pairs (a,b) and (c,d) are "equivalent" if there exists a non-zero real number x such that c=a*x and d=b*x. This is an equivalence relation. Let "a/b" denote the class of (a,b). Let the "product" of "a/b" and "c/d" be defined as the class of (a*c, b*d). Let "nullity" be the class of (0,0). Is there something more in the nullity theory?

Mark Johnson
Can we invent some new letters to the alphabet as well. Sorry but "making up" a new number does not solve divide by 0. The answer should come out as an error and thats the way it should stay.

its me
I too have solved an old age problem. The meaning of life which I call Liath. It is quite simple now that we understand that Liath happens between Life and Death ;)

Nathan Gerber
So ok if this is solved, just how do I take this new value and continue solving a problem? Basically all this is doing is taking away a "divide by zero" error and replacing it with a "nullity" or "negative infinity to positive infinity" error.

Wow...some loooooong explanations there. 0 is something we made up. dividing by 0 (for example, dividing 9 into groups of 0) would get you infinity. So you start dealing with kinds of infinity, which is also a concept, not a definable value. Zero and infinity are artificial, and they help us represent and work through problems. Like someone said down there, math is all definition. There isn't a "right" answer unless it fits these definitions.

Hyperbole. I had to show more proof in grade 5 - but I suspect this quack has no proof.

Stephen Leary
0/0 is Not A Number. This is well defined in computing science/Maths etc. "Nullity" is just a redefinition of this and has been around for years.

Nice joke. But you can't put a quantity on Nothing, that should be just about Obvious to everyone around here

Carolus Holman
If I take an Orange, and divide it by Noting or 0 or don't cut it, I still have a whole orange. So in my layman brain 1 orange divided by nothing is still an orange. I am surprised that the British are so gullible, but then again, I am British.

Dr Anderson has done nothing but add a new notation that was not needed. His definition of 1/0 as Omega is flawed, as there are larger infinite numbers. Modern computer programmers use exception handling to manage the "divide by zero" error, and this "new" concept adds nothing to that science.

Cracked out wino
Dude, Nullity RULZ!!!!1111@#$ Professor smart guy for preZ!

Stuart Hard Man
This guy needs to harden up. Seriously Plus Lee and Bag do some work!

Story Problem
There are twenty apples in a bag. Neither Rick, Jane, Sam or Betty want any of the apples. How many apples does each person get? 20/0 = nullity Each person gets nullity apples.

Bored of Education
Sorry, this guy is a fool. Nullity is not a real number, and you cannot reach it from dividing by zero BECAUSE YOU CANNOT EVER DIVIDE BY ZERO TO BEGIN WITH!!!

ummm real player? are you serious?

This is just stupid, nothing has changed, we just now have a name for the no non-value that results. You may as well call it error so that at least the calculators are still right

C R Hulcher
Zero is a place holder, never was a "number"!!!!!

This is not unlike astrophysicists who, when their numbers don't work, just theorized something they call "dark matter" which does nothing but fill in the gaps in their equations.

So many comments here from the computer programmers' camp - how many of you can honestly say the computer languages from which you draw your examples are mathematically rigorous? When was the last time a mathematics prof wrote "Type mismatch" on the blackboard? A bit of reading up on e.g. Peano arithmetic is needed before challenging Dr Anderson's working.

de Graaf
So... does this yield an answer for the Le=orentz-Fitzgerald equation (that yields a division by zero when the velocity of an object matches that of light)?

Hmmm.... I have an insolvable problem. I KNOW! I'll just make up a brand new irrational expression and claim that that is the answer! His step-by-step "detailed" example doesn't solve 0/0. He just gives a convenient placeholder instead of an error message. Also how can he call "nullity" a number if it doesn't fall on the number line? Heck I could say an apple is a number now and use his same logic to validate my theorem.

Gunnar Greger
Divide infinity by infinity: Infinity/infinity=0, or is it? Think about it. 0/0=Infinity or is it 1? The solutiuon is hidden in infinity?

Peter Tettweiler, Hamburg, Germany
to be honest: no!

Shady Tarek
Is there any practical problems solved with this ? I mean ok there's a new number now what does it do !

Matt Fletcher
Extending the field of number by adding special elements (e.g. infinity) is a basic and trivial operation in alegbra. There is absolutely nothing new here at all. The BBC should only report scientific advances published in peer-reviewed journals. Anderson's work seems only to be released via his personal webpage where his paper supposedly demonstrates "the possibility of division by zero and challenges the reader to accept it". Not the usual wording for a technical paper with something genuine to say. Please stop giving this nut free publicity.

Just do what I do - when in doubt what do you get if you multiple 6 by 9? 42. (And for those who don't see the connection - 6*9(base 13) does indeed equal 42 :) Thank you to the late great Douglas Admas for that Gem. 1/0 or 0/0 will remain NaN for a long time yet. Until C supports nullity - no computer will stand a chance of understanding the concept at the basic operating system level.

Alexander Rozman
How does making up a new symbol solve the problem of computers diving by zero? Just how does this theory suggest encoding nullity in binary or performing arithmetic operation on it?

This is great, but I don't get it, can you write a job aid for it?

Morten V Christiansen
I am not sure what Dr. Anderson has done, but in principle the idea is not problematical. Several non-standard interpretations of number theory exist, some with infinite sets of "alternate zeroes" or infinitissimals. They are provably as consistent as standard number theory. This is no different from non-standard set theory or non-euclidian geometry. If Dr. Anderson has created an proved the consistency of such a system, which is accessible enough to be understood by school children, I think that is a very nice accomplishment. It does not revolutionize mathematics, but it is very nice work.

This theory looks itself a lot like the own result it referes to: a nulity. "A" quantity, even if abstract, can be defined, not "Any" quantity. amusement but not original. math already owns a symbol for "Any value": it's a capital "A"O upside down.

Dr. OH RLY Obvious
To: Dr. Obvious, If you times a irrational number a rational, you get a irrational.

The 2nd step before the latest is false (1/0 is impossible). And 0/0 is impossible too. (sorry for my bad english, i'm french)

Tim Pozza
Will the new number allow us to calculate when infinity touches itself in space and in time?

Not a Number is basically like a workaround to keep an application from crashing a virtual software engine. That's about it. It's not a mathematical proof of anything. Basically, all he did is to propose a method that can be used in divide by zero situations, that's it. There's no reason for almost all of these chest thumping replies. It is true, though, that this probably isn't going to magically fix software glitches of any kind in modern managed code. Maybe it would allow lower level code (assembler, c, etc.) to not have to catch divide by zero errors on systems with updated firmware that handles the concept of "nullity". That's about it though. The problem then becomes backward compatibility. ;)

Michael Clayton
Quoting the Dr. Anderson "It is just an arithmetical fact that 1/0 is the biggest number there is.". That is plain RUBBISH. Patently FALSE. Here's the proof: 2/0 > 1/0

Having 0/0 as undefined is useful as you can't use it. If you define it as a symbol people use it in algebra and you end up in all kinds of 1=2 kinds of problems, throwing out an error from your calculator is a good sign you made a mistake and should go back and fix it.

I'm relieved to see that his PhD wasn't in mathematics. That said, the respect that the title "Doctor" brings should be used wisely, and certainly not in misinforming the general public, let alone vulnerable children. This made me very angry indeed, to say the least. Angrier still, when I read his papers on "transreal analysis". Again, I'm glad that these won't be published in any respectable mathematical journals. What he has done is not mathematics; it is more closely related to the field of linguistics: don't have a word for something? Let's make one up and then use it to explain the same word. He has decided that the problem of dividing by zero can be solved by saying that if it could be solved, its answer would be "nullity". Ignoring the fact that nullity then breaks most commutative laws, he has not used nullity as a method for solving any real problems. Some have said that his "work" is analogous to the discovery of the imaginary number i (the square root of -1). However, i is useful in solving many mathematical and real-world problems; nullity certainly is not. His papers claim to invent a new form of arithmetic that allows the use of his new number, but in reality they simply add axioms to the existing set so that he gets around the problems thrown up by nullity. Furthermore, he envisages the computers of the future using his new form of arithmetic so that the "NaN" error is replaced by "nullity". How does that solve the problem? Even if the computer then knows how to use it in equations, it won't give any reasonable answers since, by his own calculations, any equation involving nullity has an infinite number of solutions. How dare he masquerade as a mathematician? How dare he waste valuable research grants on a something so useless: something that, unlike true mathematics, has no scientific, philosophical or practical value? I am happy to see that there are an overwhelming number of comments on this page ridiculing his work - most of these people probably have less education than he but they can easily spot the fallacies in his utterly ludicrous, crackpot theory.

cies breijs
"-Inf" and "Inf" are no numbers, so "Nullity" is not a number ("NaN") aswell. We could make a difference between different "NaN"'s and call them "-Inf", "Inf" and "Nullity", but will this make sense? We we be able to do somehtings that was previously undoable (like complex numbers enable us to do)? I don't think so: NaN + 1 = NaN NaN * 2 = NaN this hold true for any NaN, so this renders them useless.

Great work! If nullity extends from negative infinity through zero to positive infinity then it is a valid answer for any problem not just this one! 1+4 = NULLITY!, the root of 123786476362783456734 = NULLITY! If this gets accepted nobody has an excuse for scoring less than 100% in Mathematics ever again, sorry NULLITY%.

All this is very usefull
Perspex machine: VII. The universal perspex machine James A. D. W. Anderson The Univ. of Reading (United Kingdom) (published online Jan. 15, 2006) The perspex machine arose from the unification of projective geometry with the Turing machine. It uses a total arithmetic, called transreal arithmetic, that contains real arithmetic and allows division by zero. Transreal arithmetic is redefined here. The new arithmetic has both a positive and a negative infinity which lie at the extremes of the number line, and a number nullity that lies off the number line. We prove that nullity, 0/0, is a number. Hence a number may have one of four signs: negative, zero, positive, or nullity. It is, therefore, impossible to encode the sign of a number in one bit, as floating-point arithmetic attempts to do, resulting in the difficulty of having both positive and negative zeros and NaNs. Transrational arithmetic is consistent with Cantor arithmetic. In an extension to real arithmetic, the product of zero, an infinity, or nullity with its reciprocal is nullity, not unity. This avoids the usual contradictions that follow from allowing division by zero. Transreal arithmetic has a fixed algebraic structure and does not admit options as IEEE, floating-point arithmetic does. Most significantly, nullity has a simple semantics that is related to zero. Zero means "no value" and nullity means "no information." We argue that nullity is as useful to a manufactured computer as zero is to a human computer. The perspex machine is intended to offer one solution to the mind-body problem by showing how the computable aspects of mind and, perhaps, the whole of mind relates to the geometrical aspects of body and, perhaps, the whole of body. We review some of Turing's writings and show that he held the view that his machine has spatial properties. In particular, that it has the property of being a 7D lattice of compact spaces. Thus, we read Turing as believing that his machine relates computation to geometrical bodies. We simplify the perspex machine by substituting an augmented Euclidean geometry for projective geometry. This leads to a general-linear perspex-machine which is very much easier to program than the original perspex-machine. We then show how to map the whole of perspex space into a unit cube. This allows us to construct a fractal of perspex machines with the cardinality of a real-numbered line or space. This fractal is the universal perspex machine. It can solve, in unit time, the halting problem for itself and for all perspex machines instantiated in real-numbered space, including all Turing machines. We cite an experiment that has been proposed to test the physical reality of the perspex machine's model of time, but we make no claim that the physical universe works this way or that it has the cardinality of the perspex machine. We leave it that the perspex machine provides an upper bound on the computational properties of physical things, including manufactured computers and biological organisms, that have a cardinality no greater than the real-number line. ©2006 COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

To me, it looks like the answer is still the same as it has been for the past 1200 years, he's just decided to draw a squiggle at the end claiming its the symbol for 'nullity'

Gunnar Greger
Divide infinity with infinity:infinity/infinity=0 or is it zero?Think about it.

Richard Bremner, Aberdeen
*Announcement* I have solved the problem of what is North of the North Pole, it's called Northity. Everyone rejoince.

Wasn't this article prepared for 04.01.2007 ?

Michael McGuire
The man is a crank on the level of the "squaring the circle" crowd. The accepted value of 0/0 is undefined for several good reasons that anyone with an understanding of topology or even basic calculus should understand. Replacing 0/0 with a special symbol would actually create more problems than it would fix. I recommend a quick look into the works of Cantor and/or Komologorov for anyone who is interested into modern theories of zero and infinity.

Wayne Smallman
Am I the only one to totally underwealmed by this new theory of nothingness? If all he's doing is making up a new non-number, I'm hardly surprised by him solving this problem. Almost any problem can be solved by just making stuff up to fit the problem. Some peer review might be more telling...

HURFEY DURFEY baby, congrats on coming up with a cute new name for an already proven concept. There isn't anything new here except a silly name and a washed up professor.

Dr James Anderson
Let me try to answer the comments posted above. I have defined a new number, nullity = 0/0. I used a symbol, capital phi, to denote that number. The symbol I use is irrelevant, what matters is the definition of the number. I’ll say a bit more about this number in a moment, but first let’s get clear what we are talking about. I also defined infinity as 1/0 and minus infinity as -1/0. This is consistent with dividing a non-zero number by ever smaller numbers approaching zero. The geometry of this arrangement is shown in the video. The number line stretches from minus infinity to plus infinity. It does not wrap around into a loop, it does not identify positive and negative infinities as opposite poles in a projective geometry (though it is possible to do that if you want to). The geometry is exactly as shown in the video. The number line stretches all the way from minus infinity to plus infinity in a straight line. The new number, nullity, lies off the number line. I drew it above zero, but it can be drawn anywhere that is not on the line. Its geometry can be understood in the same way that the number i, the square root of minus one, can be understood. All of its algebraic properties can be drawn as pictures in co-ordinate geometry. Some people use j to indicate the square root of minus one. The symbol does not matter, what matters is the definition of the number. Once I understood the geometrical picture of the new numbers and understood how to operate on them as fractions, using pencil and paper methods, I wrote the whole lot down as logical rules or axioms. Dr. Andrew Adams from Reading University and Dr Norbert Voelker from Essex University helped me develop the axioms. Norbert translated the axioms into higher order logic and used a computer to prove that they are consistent. The axioms contain the whole of standard arithmetic. This is very important, it means that anything that can be calculated using standard mathematics can still be calculated, but now it is possible to calculate other things as well. I’ll say a bit more about this later, but right now let’s see why nullity is a number. There are many ways to think about numbers (and I use whichever way is convenient at the time), but one of the simplest is to say that a number is anything that obeys all of the axioms of arithmetic. Therefore, nullity = 0/0, infinity = 1/0, and minus infinity = -1/0 are all numbers because they obey all of the axioms of my new arithmetic. I think the world has settled on oo as a symbol for infinity, though aleph and omega are also used for different kinds of infinity. If you want to run a competition to find a better symbol than capital phi for nullity then go ahead. If it’s a nice symbol I will use it in my scientific papers. In my axiomatisation it is defined that infinity is greater than zero. From this it follows that infinity is greater than all numbers. I’ll put a proof at the end of this message, but let’s be clear on what this means. The property of being infinitely big follows from the fact that a positive number is divided by zero. It is not necessary to define infinitely big by any other means. It is not necessary to use calculus or set theory to define infinitely big. It is not necessary to use any philosophical concept of bigness. It is just an arithmetical fact that 1/0 is the biggest number there is. As I said, there are various kinds of infinity. It is possible to add these to the number line. They are all smaller than 1/0. In some areas of mathematics a biggest infinity is defined according to the axioms of that area. Several areas of mathematics use the symbol capital omega to denote the biggest infinity. Its properties depend on the axioms in use so they can vary from area to area of mathematics. My infinity shares the property of being the biggest infinity, so you can use capital omega as a symbol for it if you want to, but the properties of my biggest infinity follow from the properties of my arithmetic and not from anything else. Some areas of mathematics define infinitely small num

Tormod H
Math is all about definition, and making consistent roules to follow in every situation. to claim that a conditional statement in computer code is fixing it; is just ignorance. with a math theorem defining how to handle this situations can improve a lot. it is important to understand that math is quite different than computer calculations; like with diffenecials, it is possible to do "calculations", but with constraints. if you break the constraints you outside conventional math and you are responible for you results. With a full proven theorem around x/0 we can change computer science too. we just need CPU-core suport, and/or define som vector rooms. Major leaps in science history is done by changing the perseption, not claiming that we can cope with it as it is. like the theroy of relativity. ( sorry for the spelling errors. Dyslectic, but not brainless :-)

MIchael Chizmar
I could not open the video so I do not know if this is relevant, but is there there a proof upon the definition of nullity? Or, is this just a rewording of what is already known, like (a previous poster stated) NaN?

Awww I solved it years ago but didn't think to publish it.. 1/0 = WTF? As you can see, my While True Float is another word undefined, and the Float lets us know it's a fractional number.

Toshke from Serbia
This is totally stupid like all similar proofs. Of course it didn't prove anything, he just created a new number, and same that number can be anything, from -inf to +inf. It is not going to help any calculations. Poor children, at age of ten, they are being taught of infinity, they should do it in high school. And this 'nullity' :( Forget it!

@ Fred
I agree how do you repersent Nullity in binary or even hex. The other problem is he didnt even solve the equation he just made up a new entity to provide a solution.. and nullity has always existed its called NULL so in essence he has just renamed the solution.

Dave Gower
This is, indeed, rather sad. 0/0 can be defined if a function that limits to it (such as sin(x)/x) is well defined and continuous. anything else, as mentioned above is simply NaN. They're not defined and probably never will be. The proof is diabolical. 0/0 = -0- therefore 0/0 = -0-. Yikes.

If the airplane divides by zero, my pacemaker crashes :-) or, the pilot has to deal with "we are nullity meters from the ground. Press any key to crash now, or wait for nullity minutes for an auto-crash" How I wish my bank divided my $1 balance by zero and told me that I have infinite money ;-)

Um, this is nothing new. We have the concept of nan (not a number) and even do arithmetic with it - any time one of the operands is nan, the result is nan. Fits nicely. So this is just a new name for something that has been around for a while.

van de Weert
In my days as a student we talked about this same problem and defined a solution to it. We called that number "van de Weert", in reference to a much disliked teacher, we had loads of fun with it. And now this .... teacher tells his students this drunk ass talk of us is true only using a different name? I call it cool, but I doubt any serious mathematician is going to take it seriously.

The solution contains 0/1 x 1/0. But his definition states that 1/0 is positive infinity. So it's 0/1 x infinity. But we all know that 0/1 = 0 and 0 x 'anything' = 0. So the solution is 0. Is it really necessary to 'make up' a new number? The truth is that he's trying to change the rules. 1/0 is NOT positive infinity! It is well understood that 1/0 is 'undefined'. I pity his students.

Brian K.
Yes, at first i thought, "pretty cool", but after reading these comments, altho many are a lot meaner than they need to be, i do see now that no problem was really solved here. I mean, if you're depending on flight systems software, you're going to have to catch a "nullity error" just as much as you would a "divide by zero" error. How would nullity propagate thru the rest of your algorithm??? Explain that and maybe i'll revise my opinion.

Tasty Wheat
If any number divided by zero equals nullity, then what does any number divided by nullity equals to? Divide by nullity error? :)

Blast Radius
The IEEE standard already defines 0/0 as NaN, which seems adequate enough. Nullity solves nothing and is simply an arbitrary designator that this professor invented. Unless "nullity" can be used in existing mathematical equations usefully, it is entirely useless. Bob has it correct when stating the uselessness of this non-number.

Computers CAN divide by zero, if they use IEE754 binary floating-point arithmetic (which practically every computer does). x/0 is positive infinity for positive x, negative infinity for negative x, and NaN (not a number) for 0/0.

Lumocolour O'Shaugnessy
Will this new fangled contraption help me get a bigger slice of a shared pizza?

I already solved this problem a long time ago. The answer is 0 AND whatever the numerator is. Where's my Nobel Prize?

Mathematicians call that compactification of the real line, nothing new!

no wonder i always flunked in maths!

a slightly less incompetent mathematician
Take a class on real analysis or measure theory. We construct algebras that can handle division by zero all the time. Dr Anderson? This "new theory" is decades old. I learned it as an undergrad, from professors who learned it as undergrads. And it definitely isn't yours.

Dr Dubey
Actually, some pure mathematicians had thought of thing quite some time ago (Sometime geometricts in the 19th century I believe).

freak guy
this is crazy..if this is passed by the international community then let me propose a theory defining infinity upon infinity as "ellipsis"..

He may be in the computer science department but he appears to be completely ignorant of modern safety critical software techniques. An auto pilot will not "stop working" if it tries to divide by zero, the software will catch the condition and try to do something sensible.

Lol! Thats just a nice joke! :-) Of course, the "nullity" number is known for a long time (it is usually called "undef") in most programming languages. The funny thing is to think that people at the BBC buy this!!! :-)))

What I find useful in his idea is that the new number could make it easier and more standard in programming languages to process results/events which are currently handled by exceptions. Plus it is always easier to use a term "XYZ" than "the event which occurs when you do this and this with that and that" - I think this is called abstraction ;) Also, the very fact that this theory provokes such a furious reaction and polarized opinions means that it IS a new idea.

We have a name for this "nullity" and have had such a name for years. That name is NaN. Learn it well, Anderson. You are no inventor, you are not heralding a brilliant and new mathematical theorem. You are simply giving a new name to something folks from the computer camp have known for years.

agree with u Caska might help the computer programing and could be interesting there.but for mathamatics not much help lol

a uk college student
Whats this guy thinking? First of all he thinks hes solved one of the most difficult problems ever, doesn't he think that any mathmatician over the past however many years has thought 'hmmm lets just make up a word for this and it'll all go away' Honestly like someone down the comments list has stated how is this to be represented in binary? I feel dreadfully sorry for the kids being taught this, many people in my previous math classes and I have said why not just make up a word for it; it doesn't work!

Tomek Perlak
Well, the concept itself seems appealing - it's just a new symbol. Just like there isn't "really" an 'infinity' - there isn't "really" a 'nullity' - but it helps to explain something. (Does it?) I would kindly disagree with Hubert J. - IMHO, there is not really a mistake in this train of thought - please, notice that this new symbol is used to "simplify" the zero-to-the-power-of-zero expression. Merely that. Anyways - I'm kind of a curious about some other expressions - can the 'nullity' be used in, say: -0- + 12 = ... ? -0- * 3 = ... ? Or are we talking here about a completely new set of numbers, almost like with the complex numbers?

Johan Krüger-Haglert
This isn't news, and it have probably been solved long ago. Java for example sets a NaN-flag when you divide by zero, NaN standing for Not a Number. Afterwards you can easily check for such cases and handled them in whatever way you think is appropriate, the important factor is that the program keeps on running instead of crashing.

defining a new symbol doesnt make up a theory

I don't think this is possible.This concept of extended real line is already there in "real line+negative infinity+positive infinity"...I don't understand what is novel about it!!!

Great, yet another headline-worthy pile of rubbish spouted by someone who clearly hasn't "got it". When will the press finally see through this rubbish and stop printing such nonsense?

I had that theory for a long time but my anwser is 1. Because if you divide x with x you get 1 as awnser. If you divide 0 with 0 you get 1. If you think like dr anderson with the power system were 0 power to 0 is 1. That the anwser.

Jyri Vedru
What is here difference from MATLAB language's symbol NaN (not-a-number)? MATLAB has been used it for a while.

Southampton ECS anonymous
You 'could' implement nullity using the "NaN" (not a number) feature of the IEEE floating point specification, having +ve infinite as 2^149 and –ve infinite as 2^-149. However, why not simply test your denominator before using it?

Ciaran Fowley
this cant be called a 'solution' as it just defined 0/0 as nullity, you call the artefact of dividing by zero nullity first, then obviously if you divide zero by zero you will get nullity (which you just defined in the last sentance). you might as well call it peanuts, not nullity.

Looks like someone's trying to get some undeserved fame. What a waste of my time watching that video and commenting on this so called theory. Come up with something that matters in the real world...not these terrible examples about heart pacemakers and plane crashes. OK I'm done.

I think I'll go down Dr James Anderson's route and call the logical result of the statement true or false 'Crapola' and thus have invented infinite compression, give me a doctorate, professorship and a massive grant now!

Kim Therkildsen
U must be joking.

Dr S.
I think its pointless and confusing to teach children something like this. Stick to rigorous maths please, not some gimmick. I think you'd need to study mathematical analysis (and know more about number systems) before being able to decide whether his 'proof' is true anyhow. Maths is an amazing subject, I would not want my teacher to make stuff up each day...

Mr Spock
The relevance of Dr. Anderson's discovery is "nullity".

When I was a boy (Here's one from the "young-whippershapper department"), we programmed aircraft simulation systems for NASA (in Fortran and assembly language). These were critical models tied to realistic cockpits that moved and shaked test pilots -- they often tried to divide-by-zero due to programming bugs, poorly-understood equations of motion, etc. So, in "real life", when threatened with div-by-zero infinities, the motion simulator didn't just smash the pilot into the cabin wall but rather gracefully smoothed the first derivative into relative calm by ignoring all digital computer output, inn favor of an analog "mechanical limiter" override.

David Stevens
I will not accept any proof that has been released on a proprietary (realplayer) codex, where is the proof!
Real mathematicians do not teach kids until the math community has verified there proof, even if this is proved to be true i think he is being very irresponsible teaching unproven methods that are not in the "curriculum" its just plain irresponsible he should be suspended pending an investigation.

Dr Anderson's Axioms: 1/0 = Inf, -1/0 = -Inf and 0/O = Nullity Using these axioms.. 0 = 0 * 0

Gerard Krupa
This man is out of his mathematical league. He has clearly based this 'proof' not on mathematical rules but on the IEEE 754 standard used in most microprocessors that defines 1/0=infinity and -1/0=-infinity. In pure mathematical terms infinity is non a number and generally considered to be unsigned. Incidentally, to deomnstrate how accurate IEEE 754 is, it also defines 0 and -0 as two different numbers. As for computing it does not matter in the least whether you represent the result of a division by zero as infinity, -infinity, NaN (Not a Number, a symbol already used in computer science to represent an undefinable result) or some new symbol made up by an academic looking for his 15 minutes of fame, you still have to handle it as an exception and not carry on trying to work out calculations based on a non-number.

FIN Anonymous
This is clearly just a joke by Dr Anderson (I hope). Actually many people probably come up with this idea of 'nullity' at some point of their lives. I remember thinking about this problem with my friend when we were 11. We came up with the same idea. Later, when reading 'real' math books at the age of 16 we learned about Riemann sphere and were extremely happy with the fact that we had come up with similar ideas earlier. If someone takes this article seriously, I hope he only considers if it would be a usefull thing to teach to children. NOT that it would have ANY MATHEMATICAL significance. I personally think that this should not be tought. Instead children should only be encouraged to ponder the problem of dividing by zero (and also other 'problems').

Hey BBC, the Innocents Day is the 28th, not the 6th. You missed by 22 days. Does any of your computers already implent this theory on its calendar's mathematical engine? Keep in mind this new is in the "People" section, not in "Science" section, so whats relevant here is the Dr doing "something", not the "something" he does. Welcome to the Yellow pages. Ok, no more joking. The Dr uses terms ment to show the limit where some sequences lead as if they were conventional numbers suitable to be used in conventional arithemtics, and this is a HUGE error. There should be some free sits on any Berkshire's 6th Form College math course for the Dr and the journalists reporting this to take advantage of.

This is stupid. Introducing a new number that would represent something is not a solution. And on the other side: Computers CAN DIVIDE BY ZERO (IEEE standard for floating numbers) - the result is a special "number" called NaN (not a number)! So this problem with introducing a new value has already been "solved" long before this (but it's not so practical) and therefore don't listen to this hoax.

Ludovic Claude
Actually there is nothing new here. In many computer languages, you have a symbol that's called NaN (Not a number) and this is the result of some impossible mathematical operation such as 0/0. The program doesn't crash when you call 0/0, it simply return NaN (or let's call it -0- like this guy did), and then it can report that there was an error to the user. So this 'number' is only something is only that's convenient to use with computers, but it's certainly not a valid theorem and has no meaning in number theory (the branch of maths that tries to explain and formalise numbers).

Just another trivial "discovery". Anybody can invent a symbol and call it a solution of a problem....

From a computer science perspective any programming language used to create software can detect and catch 'divide by zero' errors. This new nullity symbol has no advantage to software. From my limited understanding of mathematics, I would think that nullity is similar to the 'i' symbol used as the result of the square root of -1.

A lot of spurious proofs for x=y where x and y are 2 different numbers rely on division by 0. Does Dr. Anderson realize that adding nullity makes makes his mathematical system meaningless? Is this nonsense being taught at the University of Reading? The Dr. should hang his head in shame.

Any computer program what runs whatever piece of equipment (planes autopilot, car, etc.) and divides by zero is poorly designed and the programmer should be fired from work ASAP :P There are error handling techniques and workarounds of the dividing by 0 problems, if you can't do that in your computer program, don't program at all.

I know how to prevent computers from crashing at division by zero: don't do such silly things.

The Joker
Think the title should have been different. Total collapse in British traffic - Professor at Reading invents the Square Wheel.

You have to watch teachers, my maths teacher tought us that there is a maximum number, I don't remember what it was but apparently if you add one to it then the result is no longer a number

george Woodrow III
This is just nuts. First off, this was not a problem for Pythagoras because ancient Greek math had no zero. It was not a problem for Newton because of his use of fluxions and infinitesimals and not the modern notion of limits. 1/0 is not infinity. The *limit* of 1/x as x approaches zero from above is +infinity. 0/0 is undefined mostly because in different contexts, it can be 1, 0, infinity or just about any other number. In computer science, there is a symbol for nullity already. It is NaN == not a number. Any well written computer program will not only deal with cases of divisioj by zero, but a host of other problems. I suggest that Dr. Anderson review Calculus, analysis, number theory and basic computer programming before suggesting that a problem has been 'solved'.

UK Anon.
A few minor points ... 1. Dividing by zero is not an "unsolved problem", it's simply undefined. It's not a question that needs answering, it's a non question. There are lots of sections of mathematics where functions take undefined values. It's not a problem; it's part of how mathematics works. 2. There is no easy way of removing these troubling points in the genereal case. Look up all of the work on branch cuts that has been done in the field of computer algebra. 3. This is hardly new, look up real projective geometry; it's over a hundred years old. 4. Whether or not division by zero is defined, and what it is defined to be has *nothing* to do with problems with computers dividing by zero. Look up NaN in the IEEE floating point standard or the divide by zero signal handler in POSIX. This has already been solved as much as it can be; it's just most programs are badly written and don't make sensible use of these features. I appreciate that not everyone has a masters degree in the relevant area of mathematics but is there any chance you could check this sort of thing in future?

If 1 divided by 0 = infinity then infinity times 0 = 1, no? I say the good Doctor has found that making a difference in the real world is a bit hard, so he comes up with this new discovery in the virtual world instead.

Alf P. Steinbach
THERE ARE NO DETAILS AVAILABLE ON THIS PAGE. Please reconsider your use of obscure video formats. That said, 0/0 is indeterminate and so not a useful concept. x/0 where x is non-zero is sometimes useful (examples I recall from 20 years ago included Lagrangian interpolation and Dempster-Shafer evidence combination). But while multiplying and dividing such entities works nicely, addition and subtraction sends you off into an infinity of new kinds of entitites, not very useful. So I gather Anderson's scheme must be guided, but it would sure be nice to know exactly what it is, which isn't possible when it's presented in that video format instead of simple text.

Thats numberwang!!


Now this is just ridiculous and helps no-one. Publishing such nonsense (as shown by numerous posters below) just contributes to the public's ignorance. Poor show.

That's not whomever he claims to be. That's Al, he cleans my pool on Wednesdays.

The result of 0/0 isn't any "normal" number. So he just made up a new one. That's quite similar to calling the square root of -1 "i". Imaginary numbers are a useful concept because you can actually make new calculations with them that even turn out to be applicable to some real-world phenomena. Can you actually *do* anything with this "nullity"? If not, then this is indeed useless rubbish. And it better be more than just saying "combining nullity with anything gives nullity" because that concept has been around for a while and is called "NaN", Not A Number.

What the heck are you all talking about? I'm Skaro's greatest scientific mind, I created the Daleks and conquered half the known universe, but I've got absolutely no idea what this is all about, even though I've had it explained "simply" to me. Teaching this to children might be very easy, but can anyone explain this comprehensibly to an adult?

Justin Smith
The problem is that a/0 is the number such that (a/0)x0=a but ANY number x0 is 0. In Nonstandard Analysis (developed in the 1960's) there are infinitesimal numbers (infinitely small but NOT 0) that can be used to define calculus without passing to limits. Perhaps this is related to that?

Dr Anderson seems to lack an understanding of maths. He's making the common mistake of treating infinity as though it were a number. There's nothing new in his "proof" at all. Real academics test their work by submitting it to journals where it is criticised and reviewed by their peers - experts in the field. Not by testing it on year 10 children and BBC reporters! This guy is a crank and shouldn't be passing on his misconceptions to schoolchildren. Or BBC readers for that matter. Don't believe a word of it.

This is not particularly helpful (or even new, at least for computing). The IEE754 standard for binary floating point arithmetic (used to perform floating point arithmetic in computers) already defines values to deal with this situation. It has a special values called NaN (for Not a Number) which allow computer programs to resolve problems like divide by zero gracefully.

Some norwegian dumb guy
I think this theory is ridiculous. The entire "proof" is ad hoc, you could easily write out 0^0 to the new expression (0/0). The professor then "invents" a number called nullity which is not on the usual number line. That is, he designates (0/0) to a value "nullity". Well guess what, it is not on the number line!

To those saying this is some kind of 'hoax': This is not a hoax. I was taught by Dr Anderson at Reading Uni while studying Computer Science. He used to tell us about his work to solve this problem.

For all of you that think that root of -1 has not got a symbol... well... it HAS, the nimber is calles 'i' and it's a Complex Number. Fukkin a+ib, where a is a Real part, and B an Imaginary part. It's basic algebra, fools.

My doubt is that by creating a new number sistem {Z + nullity} or {R + nullity} you should redefine the basic arithmetic operations and verify (for example) that they constitute Abelian groups just like their standard behaviour in Z or R.

Ok, I am a programmer and far from being a mathematician, but here is how I have always pictured something divided by zero. First, let's do division by a real number. I have six apples, if I divide those apples into 2 baskets, I am left with 3 apples, or to be precise, 2 baskets with 3 apples in each. Basically, I created 2 groups of 3. Now, using the same six apples again, what if I divide those apples into 1 basket? I am left with 1 basket of six apples. I created 1 group of 6. Ok, simple. What if I divide the apples into 0 baskets? Well, I would not be creating any groups at all, so I would have no groups with no apples. I do not have a basket to put the apples in, so I am left with 0 baskets of apples. To me, divide by 0 and you get 0. Same as multiplying by 0. If you are creating 0 groups, there can't be anything in the groups since there are no groups to put anything into. Seems simple enough to me. I think the problem lies in the underlying logic that calculators and computers use. As a programmer, I always check to be sure the I am not dividing by 0 before actually doing the division. A lesson learned the hard way. So if I have x divided by y (x/y) I first do a simple if statement on y (if y > 0 then x/y) to keep from encountering errors. Just had to add my null cents. :)

Tom Knight
A computer scientist came up with this, not a mathematician? Sounds a little hokey to me...

personally, i think there is absolutely nothing in such new fangled gimickry

Ok, having just seen the video clip of his "proof"... I would say that he's just re-defined the statement "x/0 = infinity" to "x/0"="nullity", where x is a real number. He might as well say "x/0=smiley face" and it'll mean the same thing!

G. Dutt
Genius. Will now explain why my bank account is always 0 when the wife's been at it.

Bonjo Nelson
But what happens when you divide zero by nullity? We need to know!

This is just symbol. What's the news? How much is nullity+5?

Nathan Skene
Before all you people go blathering on with your tirades and rants, you may want to stop and consider that this guy is a professor in a good department. He has actually thought about these issues, there are many applications of these, and he isnt doing it for no reason. You may wish to go look into the Perspex Machine, Perspex neurons etc, the list continues onwards. Or you may be enjoying your ignorance.

Inventing new numbers, that's just cheating.

If I have one apple and I give it to no-one, how many apples do I now have?

John Pearcey
Complete rubbish. Zero divided by zero has answers depending on the situation governed by the functions close to zero used in each particular case. These have been solved by Newton and indeed he developed the theory of calculus to solve such problems.

Matthew Sealey, Genesi USA, Inc.
Computers divide by zero all the time; they don't crash if you can catch the CPU exception it causes. And if you catch the exception, the value you get back is already a mathematical standard - NaN for "Not a Number". As far as I can see this performs the same use but makes Not a Number a real number, but a practically useless one. As a computer science 'professor' he should already know this, and see that there is absolutely no benefit to defining a whole new 'not a number'.

I keep popping in and out of the future. There's nothing cool about this. You've killed us all.

Chuck Norris
I could have told you all this years ago.

I am absolutely furious that a respectable broadcaster suchas the BBC would lower itself to publicising this nonsense. There are any number of flaws I could point out in this guy's 'work', but I shall stop at just the one: His 'proof' that 0^0 = -0-. In the final few line he uses the reasoning (0/1)*(1/0)= 0/0 = -0-. However, You can just as easily say (in his twisted world of artihmetical fallacy) (0/1)*(1/0) = 1/1. And furthermore, if this concept is so rigorous, simple, and useful, why can't we have video of him teaching it to people who actually have a level of mathematical understanding? Mathematical professors? Hell, even university students? Oh right. Then they would laugh in his face, and that would hardly make for a sensational science story for the BBC now, would it?

I have a theory as well - Majority of people are bit stupid, pardon. So by analyzing the comments, I find 80% negative and 20% positive(do the math). He did tie number line together! Publicity he got is bad, why? He gets both criticism as well as demonstrates this solution to majority for any chance of adaptation if things are right...Some comments especially look like from medieval times, where if one would say to you- EARTH IS A SPHERE! would get response - THAT IS PREPOSTEROUS, ITS FLAT!... Think about it


that FOOL he will destroy us all ;_;

Seriously, computers have been able to deal with floating point divide by zero for a very long time, resulting in inf, -inf, or NaN (not a number) respectively, which are all valid floating point values according to IEEE 754. Calling NaN nullity is just putting a new label on it.

This work is artifical. Why? The Dr is mixing between symbolic definitions and true(real world) computations, i.e 1/0 (def)= inf; doenst represent the real world infinity which is uncountable.

Andreas Marschner
In the field axioms you can read: To every element x from F without {0} there is a inverse called ((x)^(-1)) (or call it like you want) so that x * ((x)^(-1)) = 1 where 1 is the identity elemet of the multiply group and 0 of the additive group. So one can say that 0 does not belong to this set of invertable elements. Its every time the same old trick to change the axioms by adding some wonderful new elements (here called nullity or something) and 'Hooray' here it ist the solution of a thousands of years old problem. Dr. Anderson, this isn't very helpful!

Mal Lansell
Computers have been doing this for years - it's called NaN (not a number). Dr Anderson supposedly teaches computer science - he should be fired.

But what is x/nullity?

Dr. Obvious
So we all know that 1/3 is an irrational number, right? Perhaps not! Define 1/3 = Lambda Now I can divide 1 by 3 and get a rational result, it's just Lambda! Oh those silly mathematicians.

Class Dunce
That's total rubbish. He didn't prove anything at all. The concept of numbers lying off the number line is already established (e.g., sqrt(-1), or i), but his number doesn't even have that rigor or functionality. I.e., nullity does not lie in the complex plane, but in his new plane containing only one number. That's the whole reason why *most* computer systems cannot deal with it. But in Maple or Mathematica it's handled quite easily as an exception. Furthermore, his "proof" circles back on itself and he uses to definition of his arbitrary number to "prove" the number.

Will Perkins
Pacemakers don't stop when they divide by zero. Divisions by zero are handled in computers by the programmers, no need to worry. This guy is practically using a form of terrorism, scaring people into believing the importance of his 'invention', to get it noticed.

Suppose x-y=0 Then 2(x-y) = 0 So x-y=2(x-y) Divide both sides by x-y: 1=2! THATS WHY YOU CAN'T DIVIDE BY ZERO

Dominic Connor
This is silly and trivial. He's defined a thing with the properties that it does what he wants. It's actually inaccurate to say computers can't cope with this, since they've had a specific "value" for this sort of junk for decades. I'm not sure why you refer to Reading as a "university". This is a place the BBC reports as closing down it's physics department because it's too hard. Lecturers at Reading should stick to folk dancing and knitting, leaving academic subjects to grown ups.

ed dekker
It seems like all calculations still stop on reaching 'nullity' so the autopilot still crashes the airplane. BTW There already is NaN (not a number) in the IEEE spec.

But the problem is not dividing by zero it's doing anything useful with the answer 2/0 = Nullity 3/0 = Nullity ect... So Nullity*0 = every possible number This was always the "problem" and it still it ...

George Ou
Are you BBC idiots qualified to review this? Have any of you taken Calculus or even pre-Calculus? 0/0 and 0^0 are both defined as "indeterminates". That means having no numerical value or meaning. This is defined in the dictionary, LOOK IT UP! This was the genius of Newton where he looked at the rates at which those numbers approached zero and came up with calculus to figure out what 0/0 and 0^0 actually mean. Not just some arbitrarily defined number "nullity".

i think he's just put a new name to error detection

Why don't they just call it negative zero or something. It will mean exactly as much as whatever other arbitrary name they choose: exactly nullity.

This theory looks itself a lot like the own result it referes to: a nulity. "A" quantity, even if abstract, can be defined, not "Any" quantity. amusement but not original. math already owns a symbol for "Any value": it's a capital "A"O upside down.

Roger McJoe
So, in other words, "nullity" is just a new word for 'undefined'?

awwww......there goes the fun of attempting to divide by zero :(

Christopher Morris
Mathematicians have announced the existence of a new whole number, which lies between 27 and 28. "We don't know why it's there or what is does," said Cambridge mathematician Dr. Hilliard Halliard. "We only know that it doesn't behave properly when put into equations and that it is divisible by 6; though only once."

what a crock of NaN

Markus F.
This new definition solves nothing. In fact, it just hinders. The professor points out that if an autopilot divides by zero, the plane crashes. Now, if an autopilot divides by zero, and gets nullity, then what? You cannot increase the throttle by nullity. Worse, still, it forces the computer to spend processing cycles carrying on working with an obviously wrong answer, rather than just correct itself the old fashioned way. This just gives a name to a problem rather than fixing the problem. An analogy would be forgetting to dress in the morning, heading off in your pyjamas, noticing on your front porch that it's rather chilly, but instead of heading back to get dressed you define yourself to be in a state of pyjamaity and keep going to work anyway.

When people need a number that doesn't exist they make them up. Negatives, then imaginarys, then infinities (Cantor's aleph-null etc) and then now this.

I won't use Real Player (same on you BBC) but from the white board in the image it's clear the good Doctor is making a huge mistake. He starts with 1/0=Infinity and -1/0=-Infinity. If this is true then, from very basic maths, Infinity*0=1 which is obviously rubbish, and his whole theory falls down from there. If he taught this at my child's school I'd be very unhappy.

A mathematician
Readers who want to know more can find the author's papers on the subject via Google. Personally, I don't rate them, and I think teaching an unaccepted (some say crackpot) theory to school kids is a really bad idea; if they start parroting this nullity business in their exams, they'll lose marks.

That's a completely circular arguament. You can't solve the problem of dividing by zero by inventing a number that *is* something divided by zero and using that. That's like saying "How many children are there in the average family", and solving it by saying that the number of children in the average family, minus one, is x, so the answer is x+1. There. Solved for all time, aren't I clever.

Johann Petrak
This guy obviously does not understand math and I am troubled by the thought that he teaches kids. Any second semester math student should be able to tell him why his little trick is not only utterly useless, but also leading to more trouble than it is solving. If this is not a hoax: please, BBC reporters, do not spread nonsense just because it comes from somebody with a "Dr" degree. Next time you will tell us about somebody who has constructed a perpetuum mobole or squared the circle, right?

Lawrence Dimery
I think Prof. Hubert J. Farnsworth has a valid point, not so sure about the wealth of amateur mathematicians getting in their own two penn'orth. The only one to make a decent point is Peter H who fights and beats Dr Anderson on his own paper-thin ground.

Ben Goodger
Nullity is equal to x/0 as much as sqrt(4) is equal to 4i. This isn't a solution to an impossible problem, it's a workaround. When you have a decimal value of nullity, I'll use it...

Dr Anderson wasn't the first to invent a symbol for a devide by 0. Computer programmers 'solved' this problem ages ago. On a computer, dividing by 0 doesn't cause aeroplanes to crash - it just gives the result as NaN(not a number).

Another name for 'nullity' would be NaN for those speaking javascript for example.

Chuck Norris
Only Chuck Norris can divide by zero!

Frenchy McBritish
This is ridiculous. I've been using nullity for years. Only instead of "nullity" I call it "socks." And by "using" I mean "wearing on my feet."

It's just the NaN made formally in algebra. Computers can already do this, and not crash at all.

Inventing a new nubmer doesn't solve anything? It's almost like NASA should say, "Well, we can't travel to Jupiter, so we renamed Mars to Jupiter. Now we can travel to Jupiter."

Karl Buys
I think he should be hailed as Professor Maths Adjectives, because he's not doing anything else besides describing the concept of how division by zero is undefined in the sense of quantitative values. We solved this problem long ago by defining division by zero as being "Not a number.". Chris Croughton summed it up earlier. If you ask me, this guy should rather try to come up with a useful theory, instead of redefining a concept such that it makes him look smart. Pythagoras would say, "You, me, in the parking lot, now." if he was still alive. Arguing semantics has no place in mathematics. Neither does a marketing team. Invent a useful theory if you want to be hailed as a professor of mathematics.

This is nothing new.. Chuck Norris could already divide by zero by roundhouse kicking his calculator first

old news, the idea of dividing by zero has been covered several times in mathematics, but with points ouside the number line, and also points at infinity, infinitessimals, transfinites and so forth, this is a step backwards, if anything, and certainly nothing new

This guy should have his brain examined. The country Sweden is laughing and asking them selfs - Are all englishmen this stupid? I think you need to change your diet!

Mr Gently
I tried this on my calculator, it just said "A suffusion of yellow". Again.

"which solves maths problems neither Newton nor Pythagoras could conquer" yup sounds like a turkey, didn't need to read the article after this

John Ryan
We have life for 1200 years not needing to divide by zero, so why do we need to know?

I define all of the world's problems as monkeys, therefore we don't have any more problems, just monkeys. Let's go see if it made a difference!

It's just a new label for the same result. Wether the computer says "error" or "nullity" the plane will still crash. "Raise the flaps by nullity%" - it won't help you land. If your pacemaker decides you need "nullity" heatbeats per minute I think you'll still dead.

Only Chuk Norris can divide by zero

Claus Tondering
Rubbish! Using his technique I can prove that infinity is zero: (I use ^ to indicate exponentiation and * to indicate multiplication. I also use the fact that 0^2=0 and 1^2=1) infinity = 1/0 = 0^(-1) = 0^(1-2) = 0^1 * 0^(-2) = 0/1 * 1^2/0^2 = 0^2/1^2 * 1/0 = 0^2 * 0^(-1) = 0^(2-1) = 0^1 = 0 Hence infinity=0. Rubbish.

Year 13 Stats Class
What a load of....We think he is giving mathematicians a bad name. We are not all sad people that have nothing better to do with cur time than make up new numbers that aren't even true!

This seems to be just another representation for 0/0 but not any solution to me. That way anybody can define a symbol to any unsolved equation and say he/she solved it.

Yeah, we can't divide by zero so we will make up a number that will allow us to...

Class 10M2
We understand it but it is totally pointless.Nobody was bothered before so why are we bothered about it now.

Jick Rames
Making up a stupid word to solves that? In that case it was done long ago and the word is "OH SHI-".

Ryan: on that circle of yours, isn't the distance between 1 and 0 and between 0 and -1 infinite as well? Being 0 the only quantifiable number in between... that makes it a focal point in the curve, which has not an inverse beside itself. Or if we force it to have it, it would have two, one below, one above. But as we step away from 0 in any of the two directions we step into infinite fractions of 1 or -1. How can you state therefore that 1/0 exists as inverse of 0/1 on the vertical line? It would be more polite to assume that 1*0 = 1/0 = 0.

2 cents
What does it solve? Call it nullity or whatever you feel like, it's only a concept, no solution. In software we deal with hard numbers. A CPU is basically a number cruncher. Nothing more, nothing less. It can't handle a concept. In programming dividing by zero still requires some extra work to handle it elegantly.

In the same way that i (square root of -1) cannot be calculated, and that infinity cannot be calculated, nullity cannot be calculated. All we have defined here is that something divided by 0 is something that we cannot calculate - a problem that still hasn't been solved for 1200 years and probably won't be for another 1200 years

I don't see anything new here. Programming languages like C++ use NaN which means Not a Number to represent division by zero. But it's safer to avoid this division rather than look for NaN...

Babel fish
Then the answer to the ultimate question of life, the universe and everything is in fact... nullity?

I remember some time ago, developing a 3D realtime engine, putting the camera looking exactly to the 0,0,0 position ended with a divide-by-0 error, I felt that something failed there, there's must be a better matematical solution that permanently adding a fraction to the target of the camera to avoid this error

Somebody was stupid enough to release this breaking news in Real video format! The Real format is not an open format that everybody can use. I read this web page its because its in HTML, which is an open format. When releasing something targeting the world, please understand the importance of releasing it in an open format so that everybody can see, read, hear it. If it is audio, Ogg Vorbis is recommended, you may consider FLAC if you are releasing something requires very high audio quality. If it is video, Theora is recommended.

Dr. Jones
It's a real pity that BBC runs this kind of news without confirming them with somebody who knows *something* about mathematics. This is just sad and silly.

Shams from Norway
The theory og nullity is nonsense! Everybody know that everything around us whether it is technically equipment, arcitectures and so on are based only mathematic. So why doesnt the socities, communities, and country fall apart if our old mathematic isnt complete, as Dr Andersen trying to tell us. I dont beleive that his theory of nullity give us significant increase og mathmatic knowlegde og give more helpful in gaining the mathematical solution. Shams B

Mike Scott
The real numbers are, mathematically speaking, a field, which means that they have a lot of useful properties that appear to be intuitively obvious (although of course they're not, you're just used to them). If this "nullity" element is added to the real numbers, they are no longer a field (It breaks either the multiplicative inverse property or the multiplicative associativity property, depending on whether or not you define a multiplicative inverse for nullity), and so a lot of useful results become inapplicable.

Nick Sharples
No, sorry. His definitions are inconsistent: His Definitions: inf=1/0, -0-=0/0 Also he claims that -0- is "off the real line" so -0- is not a real number. From his calculation: -0-=(0/1)*(1/0) But: (0/1)*(1/0)=(0/1)*inf = 0*inf (by his definition of inf) and inf=1/0 implies 0*inf=1 Therefore -0-=(0/1)*(1/0)=1 Therefore -0- is a real number, which is a contradiction. This refutation doesn't use any abstract notion of infinity, or uses any of the highly analytical mathematics required for dealing with problems of Dr. Anderson's type. Instead it only examines the mathematical consequences of the definitions that Dr Anderson provides. When introducing definitions in maths, only two things are required: The objects aren't defined ambiguously, and the definitions are consistent. Without consistency, we can 'prove' anything in mathematics.

It all boils down to the sum people, understand that when you have nothing, something is better than anything. So this nullity gives you 0}0.0 = [´0.1 wich is indeed a new number, just go with it.

in hex, there is no zero, it is a set of 16, and the grouping is defined by the digits (16). in decimal, the zero is used as a placeholder for the grouping mechanism. In reality, zero does not exist. we use zero as a placeholder in our math, of the 10, which is a group of x * 1. or 20, which is x * 2. but the 10 is now a number itself, which creates a number of the placeholder, but still this number does not exist. I feel this is a rudimentary problem. why create something out of nothing, to solve a problem we created in the first place?

Bob Bobberson
How about it being as simple as this. 0 = nothing, correct? So saying 1 divided by nothing is as simple as saying 1. 1 times nothing is 1 nothing, which equals nothing. Why does this have to be difficult?

So as you divide by smaller and smaller numbers you tend to infinity, but when you reach zero it becomes nullity? Its stupid. What happens when you divide by nullity? This solves nothing, this man is an idiot. So we will just rename a divide by zero exception to a nullity exception? You can't do anything with the value nullity.

Newton did solve this problem with calculus. dx/dy give the gradient of a curve at a point, which is done by making dx and dy equal to zero. Unlike Dr. Anderson's work, Newton's is actually useful for something.

I suppose Dr James Anderson is a medicine doctor, because noone slightly familiar with mathematics can come with a theory as lame as that. It's just the same as claiming that giving name to a certain disease cures the disease.

I think if an airplane's airspeed or altitude wanders off the real number-line, it's in pretty serious trouble regardless of whether it calls the result nullity or not. And programs don't crash when they divide by zero unless they're *really* badly-written; for a CS professor to suggest that they do is bizarre.


I thought it was only chuch norris who could divide by zero

Hmm. Any number divided by 0 is nullity? Interesting. So 1/0 = -0-. 2/0 = -0-. This gives us 1/0 = 2/0. Multiply both sides by 0, and 1 = 2. Why is it that Reading University attracts all the crackpots?

Chuck Norris
I can divide by zero.

Dave Taylor
0/0 = (1+[-1])/0 = 1/0 + [-1]/0 = 2/(2x0) + [-1]/0 = 2/0 + [-1]/0 = (1+1)/0 + [-1]/0 = 1/0 +1/0 + [-1]/0 = 1/0. So nullity = infinity = [-infinity] (by a similar argument). Moral: Doing basic algebra that involves division by zero generally produces nonsense. Mathematicians already have ways of handling infinity and division by zero, which are treated very carefully to avoid stuff like this.

Well, I think that the point that the Doctor is trying to make is that 0/0 = , and all he wants to do with nullity is to make sure that you get one thing which means "any number". This will probably make life easier for computers. I'm not so certain that it makes life easier for the children at Highdown.

you cant divide a number by a number and get an absence of number-and-type (which is what null is). It's undefined. And no this will not solve programming problems, it just moves the problem on a notch to the next level. Plain Stupid, -1 points.

Pete Morgan BSc
HOAX. So what is Zero to be then. Apollo would now be permanentely on the launch pad if 5, 4 ,3, 2, 1, nullity .. so we sit here forever. And as a programmer myself, we already got a workaround for div/0 errors. Almost 99.99999% of applications do. This is pathetic and am surprised the BBC has been mug enough to make a feature of it. Please remove this nonsense ASAP.

O_o oooOoo.. like i care??

Computer Professional
Has this actually been published in a peer-reviewed journal or has this only been subject to review by Year 10 children and gullible reporters? Are there any meaningful results when operations are performed on this new number? Does associativity hold on those operations where it would hold with other numbers? If not, then it isn't a number. Offhand I would say it either looks like something useless, or as someone else has already pointed out, no different than the NaN that computers have used in floating point math for 30+ years.

HAHA.. u cant just start a new mathematical invention.. since it has not been figured out in like 1200 years, and now suddenly this "dr anderson" invents "nullity"? its weird.. its not strange dat nobody has ever figured this out, since they didnt think about "the fantastic no-problem nullity!".. strange!

The solution to x=1/y as y tends to 0, is that x tends to infinity. The solution to x=-1/y as y tends to 0, is that x tends to negative infinity. The solution to 1/0, however is undefined. You can indeed just make up a number and define the solution to be that, but it's not terribly useful. Compare this to the square root of -1, which although equally unfathomable, has been defined as 'i', and actually has some use.

"Computers simply cannot divide by zero" is wrong. Computers don't implement math (for instance they have a limited integer range) and the handling of n/0 depends on the processor. Sometimes it's NaN as another poster mentioned and some processors like the PowerPC allow intiger division by 0 (n/0 = 0)

Every time I divide by zero, I just get "oh shi-" on my calculator.

Tony (Cambridge)
The good news is, that whenever we have hard to solve mathematical problems, it's no longer difficult. Just invent an new number.... problem solved... this should advance mathematics infinullitesimally.

Hal Jordan
Funny how he picks Green Lantern's symbol for nullity.

Salim Siwani
The concept isn't new. Computer programmers have been using the idea for years. To make software robust you have to check to see if your about to divide by zero. If you are, then simply return a sensible number in its place (I use 1.0 most of the time). A divde by zero usually comes from some error condition and returning a sane number back usually gives you a stablising effect that means your software won't blow up.

I like this theory, it just isn't a solution, just another way to ask the question. For me(and I think most others): x/0 approaches infinity, x^0 = 1( by definition), 0/0 = 1, 0/x = 0, x/infinity = infinitely small (very close to 0) These work always unless you take x=0, then is is 0/0 = 0,1 or infinity, but when will you do that?

Haakon Bernt Eilertsen
Dr Anderson has not provided anything that is unknown to a good student of functions. Since some functions are irregular near some points as the denominator tends to zero, we may introduce a new ambiguous number (variable)which may satisfy any equality with "old" numbers. This new number solves all formerly called indefinite expressions and undefined expressions 0/0, 0 to 0-th and so on.

Well it's just the same principle as the square root of -1 being the imaginary number i, nothing to see here please move along...

Jim Moores
A lesson in how to embarass one's self and the BBC internationally by not checking that your ideas aren't stupid with the Maths department down the hall.

Duncan Loriander
This 'theory' is as much nonsensical rubbish as timecube theory. And at least timecube theory is funny as all hell.

There are so many problems when he tries to solve the problem. The expression (0/1)*(1/0) cant be turned into 0/0 since 1/0 is infinity and we can't use the ordinary simplification rules that we use for fractions. It totaly alright to introduce this definition if it makes math better, but since it only is humbug and full of contradictions, it is of no use. It must be of limited use in computers also, you can check for division by zero and use exception handling. There's really no need for this.

Taxpayer Norway
Apperantly, the tax offices here in Norway has known how to devide by zero for many years... They reall do!

Read slashdot about Dr. Anderson

Ijonas Kisselbach
Computers have always been able to divide by zero. The result is always "divide by zero error", which is no less useful than "nullity". Its all in the interpretation.

arild haraldsø
it`s easy..thats it!!

Suprised American Mathematician
Wow, that has got to be the /dumbest/ idea I've ever heard. Thank you, Britain, here at Texas A&M we in the math department would have hung this guy before he could make a mockery of his school. I'll remember to ignore math papers from the "University of Reading."

Seriously, He created a term for something and then said it exists... HAY GUYZ... LET'S FIX THE PROBLEM HERE 0/0 = &#612; OK? why?!?!? well cause... it is!

So 0/0 has been given a new label - nullity - and other fractions with a zero denominator can be expressed in terms of that. I don't see anything new or practically useful from this. The theory of complex numbers (which is extremely practically useful) came about in a similary way though - call the square root of -1 'i'. Can anyone see this mechanism yielding similarly useful theories? (I can't myself).

I did a paper on this, as a sophomore (I think, Im went to a swedish school). I introduced some silly symbol representing 0/0, then I used it to solve tan(0) and some probability equations proving I was a superhero somewhere in the universe... I got a c- :)

Haakon Bernt Eilertsen
The solution proposed by Dr James Anderson ought to be well known by anybody with knowledge of real functions and their behaviour near points of discontinuity. As the denominator tends to zero, the function value may tend to infinity or any number depending on the particular function f(x). So simply define a "number" (actually a variable)which may be interpreted as "any number or infinity". Then as is well known, the problem of dividing by zero is solved. The important issue is the new weak equality between the new number and any old number.

This is just a horrible paper based work around that isn't required. There are already enough ways of handling this. Computers have divide by zero exceptions , and us meatpiles have infinity.

This brings us to the question: "Is a workaround a solution?"

Either this guy is an joke or someone just misunderstood him.

Any number divided by 0 tends toward infinity.. given that infinity is one really big number I cant see this solution being much use in computing without being either wrong or highly inaccurate. (1/1 = 1, 1/.1 = 10, 1/.01 = 100 ... and so on down to 1/0 .. maybe a graph might be a better form of explanation. you could ever put superman on the end of the line flying off into the wild blue yonder.)

1/0 why is that always regarded as positive? If we approach 0 from left hand side, then it approaches -infinity.

Simple logic :-)

You can't divide by ZERO, so in my very humble opinion no action is made on a number that is being divided by zero, so: 4/0 = 4 (no action taken on 4, since dividing by 0 is impossible) That imho would solve the problem.

Ed Loach
In his workings Dr Anderson doesn't only define "nullity" as a new number - he also defines 1/0 as infinity and -1/0 as -infinity. The answers to these two calculations are undefined, otherwise you can also prove 2 = 1 (2 = 2 * 1/0 = 2 * infinity = infinity = 1/0 = 1). Infinity is not a number (and indeed there are an infinity of infinities when you get into the maths...)

You can't just add something in to fix the problem that is just bending the rules. If I had of tried this in an exam, complete with a justification, you know it would have been marked wrong and you would have been burned at the stake for even trying it

This is similar to the the invention of the number i sqrt(-1) which has all sorts of practial applications except this assumes negative infinity exists which I do not believe has been proven

Patrick Bampton> A 'RAM' file is a Real Media file - the same as used all over the BBC news website for audio and video.

Ugh... The British are at it again...

Excellent, this is fantastic news! Who wants to join me in pursuing a multi-million dollar research grant to flip the world of mathematics on its head AGAIN by proving that "nullity" equals zero?

Simon Day
So if this new "nulity" line sits perpendicular to the real number line, then where does it sit compared to the imaginary number line? Are we now going to have Anderson space as a 3 dimension equivalent of Cauchy-Riemann space?

Haha :-) What a funny story! It's not even the 1st of April!

Per Jensen
Name it what you want, it's still dividing by zero. I used to teach computer science, and when we discussed zero division I used almost exactly the same "proof" as a joke. Funny maybe, but brilliant it's not.

For anything to be useful, one must be able to do something with it. How can this 'new' number be put to use? e.g. the concept of 'imaginary' numbers ie. sqrt (-1) can be useful in advanced calculus. So extending the idea of use, what can nullity be used for? Is it, as people have said, just something that someone has chosen to name?

That guy is trying to be smarter than he is. His theory is plain stupid. He should try this instead: a^2 - a^2 = 0 -> a(a-a)=(a+a)(a-a) a=a+a a=2a 1=2 (!) or 0=1 Now i proved it :o) you can easily devide by 1 instead of 0. :o)

Mr Anderson's still living in the MATRIX world. This is just not possible, assumptions can provide solutions to many unsolved problems which still end up being problems unresolved. Like I'm assuming him of not being a doctor.

Could he not explain it on the website? Why do I have to watch a silly real player video?

There are three main problems here. The biggest one is that "nullity" is homomorphic to "indeterminant", so he hasn't solved anything just gave it a new name. Further problems include 1/0 not being infinite (this cannot be goten around with either limits or more basically epsilon-delta), and that he has claimed also that 0 x infinity = nullity, which also isn't necessarily true.

I agree with Sam

Christian Bau
Computers can't divide by zero? Please tell that Professor Kahan. And maybe the guys at the Institutie of Electrical and Electronics Engineers at need to be told that something is missing in their IEEE 754 Standard for floating point arithmetic that about every computer since the mid 80's is using.

J. Tvorup
Through history, many geniouses have been laughed at for their theories simply because it couldn't be right. Some years later, they were proven to be right. Therefore I normally would give the idea the benefit of the doubt, but this simply does not make sense! If I have a cake, and I would like to divide it between zero people, how large a piece would each person get? It does not make sense. I admit, I do not make aviation software, but I do believe that it is the normal procedure to catch the divide by zero exception , have the software ignore that calculation (or whatever your strategy is), and recalculate. Maybe give an alarm to the crew so they can take over manually. In any case, it would be much easier to handle an exception than some number we don't know between negative infinity and infinity!

Norsman says
the only new to this - is that you gave a name to what is impossible - and you put the impossible correctly away from the numberline - where it belongs .. rubbish

no matter what you say, 0*0 still equals 0. nullity, as defined by 0 is still, nothing. and if you divide, multiply, add, etc, 0 with 0, you still have naught but 0. nullity as defined by O, as a variable could provoke some interesting answers. (note the 0 vs O, (or 'o' if you don't use caps)

gregory haines
hehe, so...x/x^2 is continuous now? on the (stealing a name, thanks 'Anonymous') infinullity number plane?

wow... didn't know pacemakers are designed to kill you by dividing by zero. Also, if you weren't aware, 1=2. It can be proven by dividing by zero.

This sounds open the door to more understand how we can apply the theory of the "science fiction" methodes. Any result much better like an error in any case, because you can do something with a result, but you cannot do anything with an error. Good luck.

i dont think it replaces the problem, as well the infinity itself is better.

Ok, so by "creating" an imaginary number, he solved this problem? Hell, I could have done that! How will this help computers? What exactly does nullity MEAN anyway? If you are dividing by zero, then find another way to do it, you probably screwed up!

Please bring news like this on the date assigned for it: April 1st

I hear we also jsut made a new colour !

Observe that Dr. Anderson carefully made sure no one in the room knew anything about mathematics before he began talking...

Almost sounds like the "i" disclaimer that goes along with an imaginary number, (the square root of a negative number). Now what is the practical application?

I've thought of this before
And it is possible...just like imaginary numbers.

USC Student
I hope this is a joke . . . a very bad and not funny joke. Nullity? How ridiculous

David Junger
JavaScript and some other languages obsoleted divide-by-zero exceptions long ago. Type one of these lines in your browser's address bar and press return to get the results: javascript:alert(1/0) javascript:alert(-1/0) javascript:alert(Math.pow(0,0))javascript:alert(0/0) For the lazy ones, here is what JavaScript returns in each case: Infinity -Infinity 1 NaN (Not A Number) three of which are special values of the Number type, and much more meaningful than Dr Anderson's "nullity". These values are not errors, they can be used anywhere numbers can be used, for example the expression -Infinity+3 is valid and evaluates to -Infinity, and Math.sqrt(Infinity) returns Infinity. Math operations on NaN simply return NaN, they don't complain.

Cynthia Gauthier
Actually, this problem has many implications, which may require or assume a different solution. For instance: [1] You have zero pie. Your task is to give an equal slice of pie to zero people. You may not give more than what you have, since you can not create pie; you may not give negative pie either. This case says 0/0 = 0. [2] As you approach x = 0 in the expression 1/x, the result approaches positive infinity. Nothing is defined for the case 1/0, since 0 has no sign per se. This case says the result is either positive infinity, negative infinity, or some kind of "signless infinity". Well... It still has no defined value. So there.

At one point he came to the formula: 0/1 * 1/0 0/1 = 0 1/0 = infinity (To his theory) so he says: 0 * infinity = nullity But we all know 0 times something is still 0.

Peter Newman
That's so easy its amazing that it's never been before!

Why not ? Why reject this ne idea and consider it "heresy" ? THERE IS NO HERESY IN SCIENCE or in maths ! There are concepts that work and some that don't. It took a decision from the Pope to make the occident accept the idea of 0 (zero) ! The number 'i' (where i-sqared is -1) helps solve mathematical problems. They _work_ ! If this 'nullity' works and helps, it might be good. If not, it will disappear.

Question: Why do we say things like 1/0 are undefined? Can't you call 1/0 infinity and -1/0 negative infinity? Why not? Answer: 1/0 is said to be undefined because division is defined in terms of multiplication. a/b = x is defined to mean that b*x = a. There is no x such that 0*x = 1, since 0*x = 0 for all x. Thus 1/0 does not exist, or is not defined, or is undefined.

Brian C.
From what I saw, all he's done is propose a method for solving zero raised to the power zero, not dividing by zero in general. What about 5 divided by zero, or 16, or any number on the real line? Now I'm not a mathematician. I'm sure there's more going on here than meets the eye, but it looks like he just grabbed a random greek letter and called it zero over zero. More explanation is necessary.

Sean Young
If the autopilot divides by zero, there is a problem in the programming. Rubbish in, rubbish out. A new symbol for rubbish doesn't change anything.

For the general case, 0/0 *should* be an error because of what it is supposed to represent. I'll run with the apples analogy: You have 10 apples, and distribute them among n people. The formula 10/n represents the amount of apples each person got. Where n = 0, there are no people to even receive the apples, and your apples have been allocated outside of the (hypothetical) universe. There are no values left to work with. I'm not a math/physics guru, but I believe there are no practical (read: real) applications for division by zero. When your computer does it, it's because of a poor assumption by the programmer, or is specifically being used to raise an exception to the given set of assumptions so that it can be handled as a special case. The only time it arises in math is when operating on computed values , like dividing by a delta -- why would you operate on a delta if nothing has changed? Finally, the person who programmed your pacemaker may have opted for a timing crystal sprinkled with capacitors, resistors and diodes. If they were expected to use a computer for some reason, they're not permitted to be so absentminded as to make the mistake of introducing such a bug. Even so, it's probably also designed to reset on failure. Hopefully the same goes for the metal birds.

1=1 1/1=0/0 1=0

I agree with Wyvern. What he's talking about is called the "limit" in calculus.. we know that [any constant but infinity]/x as x begins to approach 0 will begin to approach infinity (or negative infinity if anything is negative). So, the limit of 2x is 10 as x approaches 5. If it approaches from the left (as in 4.999) it will become very close to 10. As it approaches from the right (5.0001) it becomes close to 10. The problem is, 1/x approaches negative infinity as we come from the left and positive infinity from the right. And since we don't know the answer, neither the limit nor the actual answer exist (I think). I'm no mathemetician but making a new name for an old problem is not a solution. And saying the answer is between negative and positive infinity doesn't help us anyways. (what Bob said).

Thanks for destroying the universe.

either HOAX or poor kids, very sad

Bob, I think you misread something. It says that the conventional number line stretches from negative infinity, through zero, to positive infinity. And not the new number, nullity lies in fact outside this conventional number line. (Not that that makes it any clearer for me, might make it clearer for you though.)

1/0 is not infinite, it approaches infinite but infinite is not defined. This man is a moron. Also you cant just define a "constant" nullity and claim to solve the problem, hello? NaN already exists as does lots of freaking error trapping values in computers.. Fuck you

this was the only concept which humans were missing and monkeys already knew. This proves to me that we indeed descended from monkeys ! Take this creationists !!!!

I can't watch the video because I refuse to use malware like RealPlayer, but I feel the need to point out that several responders have misunderstood a poorly-worded sentence in the article. The article does not state that nullity stretches "from negative infinity, through zero, to positive infinity". It asserts that as an explanation of *the number line*. Read the sentence again, and you'll get it. I too made a double-take on that sentence, but it's not stating anything as hair-brained as some of you are suggesting. I do completely agree with David, though. This won't let us solve anything we couldn't before. It's simply a notational convenience which allows certain mathematical patterns to be expressed more succinctly.

Peter H: His theory doesn't work, but your math doesn't show it. The problem is with "But, if 1/0 = infinity, then it stands that infinity * 0 = 1". To get from the first to the second, you need to multiply by zero, so 1/0 = infinity 1/0 * 0 = infinity * 0 NOT 1 = infinity*0 BUT 1 * nullity = infinity * 0 nullity = infinity * 0 It's well know that defining a/0 to be any real number allows you to show it to be every real number (thus all reals are equal), which is why dividing by zero is typically undefined. His nullity is not a real number, though. Basically, you take all the rule of algebra and make them only work for real numbers, and treat nullity and the infinities specially. Gee, that sounds awfully familiar. Almost just like a limit, in fact. In calculus, the Laws of Limits allow you to manipulate limits (which can involve infinity) using regular algebra as long as they don't involve infinity. There are certain indeterminate forms, like 0/0, which you can't manipulate in that way. Those require special treatment and yield different results depending on the problem. Leaving aside the matter of defining nullity in a way which doesn't break the rest of math, how useful is it? I have to agree with most others here that it's not. It doesn't represent anything in the real world, which takes away any immediate uses. Neither does i (sqrt(-1)), but there's a difference between them: most algebra still works for i. (sqrt(a*b)=sqrt(a)*sqrt(b) is the only rule I'm aware of which requires a and b be real.) Almost nothing works with nullity. So, nullity is a new "number" which doesn't represent anything real and makes almost all expressions containing it unmanipulatable. That's why his theory (not a theorem, as the article states) is pointless.

Christer from Norway
If the solution to a problem is to create a new number then he is correct. But how to divide nullity to nullity. Stupid man

Tore Sinding Bekkedal
The remarks about the computers is patent nonsense. I'll try to explain this without getting too technical: When a computer encounters a division by zero, it is called an "exception". This leads to the processor jumping into some program code it has ready for the purpose of handling this. Now, this code is written by the user. If a normal program in a normal environment gets this error, the program which executed the errant instruction will be closed by the operating system (Typically Windows, alas) - this is one of myriad sources for the infamous "Program X has executed an illegal instruction" dialog box in Windows 95/98/ME. However, in a special-purpose and mission-critical applications, which both air planes and pacemakers most certainly are, there are exacting standards specified regarding how this is to be handled. Typically, such an operation would have absolutely no effect to the user (the system would immediately recover from it), and the example of the pacemaker is completely absurd. That this comes from a professor leads me to believe either that the article grossly misrepresents his statements, that this is a hoax, or he is clueless.

Simon the Austrian
Gosh, what a Hoax. One can't just define that infinity equals 1 divided by 0, whats with 2 divided by zero? what pupils should learn in school is that never ever infinity equals another infinity. Depending on your definition of infinity (there can be infinite amount of different infities created by something divided by zero) you would get a different result for nullity for each definition.

UW Student
How is that useful though. i (or j if you are in EE) is useful for describing sinusoidal circuit behavior, also, using i*i you are able to arrive on the real number line again, making previously undefined problems solvable.

Just a new name for an old thing. This this does not help. Probably the urge to name something in order to be able to -pretend- to understand it.

If you think of it in logical terms, say 5 is divided among say 5, then we all know that each gets 1. Now if we do the same with 5 divided among 0, that must mean that we either think of it as each gets nothing since no one is to claim "their share" or 5 since it has not been divided into any new pieces. So, as i see it we have to figure out a convension saying which is to hold. Nullity is pure bullshit (please excuse my french). But then again, my own theory will not hold for long, just like Dr James Anderson's theory. Another possible value of X/0, for any X is i. But i as we all know is not a valid number.

As someone else in this comment board said, the fact that somebody proposed the special number doesn't make it "real". In fact, it's demonstrably not real because it sits someplace off the real line, in a plane that could be called the "nullity plane", somewhat akin to the "complex plane" that's composed of the real numbers smooshed together with the value i. Then, of course, you can smoosh nullity, i and the real line all together and get something in 3-space that appears very, very strange indeed. It's probably the place where you can hear one hand clapping, and there are lots of trees falling with no one around to hear them.

if I woke up one day and just made up some nutjob theory, could I be in your news too?

Scott Lamb
Every calculus student knows the answer to such questions as "what is the limit of 1/x as x approaches 0 from the right" (positive infinity) and "what is the limit of 1/x as x approaches 0 from the left" (negative infinity). And more usefully, such questions as "what is the limit of (f(x+h)-f(x))/h as h approaches 0 from the right" is the definition of derivative. Integrals are defined through limits as well. This is the very foundation of calculus. But "1/0" alone? What does that even mean? There's no answer. It's a stupid question. The first thing he wrote - "infinity = 1/0" - was already wrong. If he made his arguments to his peers instead of schoolchildren, they'd shoot him down, and rightfully so. Furthermore, saying that computers cannot divide by zero shows a ridiculous lack of common sense. They can do anything we design them to do. Many computer number systems have a special value "NaN" (not a number) that is similar to his nullity concept, except that it's not arrogantly proclaimed as revolutionary or a solution to every problem. Generally, asking a question such as "1/0" indicates a serious logic error. Imagine that airplane needs to calculate the proper elevator trim. Oh, great, the answer is nullity. What does that mean? How should it move the elevators? Giving this failure condition a new name doesn't change the fact that the airplane's still going to drop out of the sky.

mike in sj, calif.
next week, the professor will explain perpetual motion.

I'm a physicist (not a mathematician). At first glance I feel cautious but at the same time it doesn't seem any worse than the concept of the square root of negative numbers (multiples of i). I'm sure Riemann would have something to say about this. Anderson could have been a bit less arrogant about it: he's setting himself up for ridicule if it is shown to be nonsense.

This is ridiculous. I can't believe this guy is a professor. Any moron can define division by zero. Here, let R be the set of real numbers. Let / be a binary operation on R that satisfies: (i) 0/0 = 17; (ii) 0/a = 0, for all nonzero a in R; (iii) a/b = a * b^(-1), for all nonzero a,b in R, where * is the usual multiplication and b^(-1) is the multiplicative inverse of b. Too bad Newton and .. Pythagoras (seriously? Of all the great mathematicians, Pythagoras?) aren't as smrt as me and Dr Anderson.

how does i divided by zero, doc?

The problem of 0/0 or 0^0 is more a problem with 0 then it is with anything else. 0 infinity and negative infinity are loose concepts. In actuality none of them exist. Zero is just a very very very small number and infinity is just a very large number in practical terms. There was only ever one true 0 which was the universe the instant before it exploded and only one true infinite which is the universe now. Everything else falls into the number line.

1. Let 0/0 = -0- 2. 0^0 = 0^(1-1) 3. 0^(1-1) = 0^1 * 0^-1 4. 0^1 * 0^-1 = 0/1 * 1/0 5. 0/1 * 1/0 = 0/0 6. 0/0 = -0- This guy isn't a genius. Between steps 5. and 6. there should be a step that says "CAN'T DIVIDE BY ZERO!" This guy didn't solve any problem.

Peter Robinson
Using Dr Anderson's methods. If we assume NULLITY exists then we get 0^1 = 0^(1+0) = 0 * NULLITY = (0*0)/0 = NULLITY. So NULLITY = 0. This is a contradiction, so NULLITY does not exist. To handle 0/0 you need to understand calculus - then l'Hopitals rule tells us that it depends on how you arrive at 0/0, so x/0, 0/x and x/x all have different limits as x tends to zero. The only mystery here is why is Dr Anderson allowed to "teach" this nonsense.

John Standish
This is just bogus. You can't divide by zero. He is just adding another term to math. It would be the same as doing this in code, returning a null object( I am giving a java example ) private static Object divide(int n, int d){ Objct ret; if(n == 0 || d == 0) ret = null; else ret = (float)n / d; return ret; } try it out. If you print the value of the object returned by the divide method it should either be null or a floating point number. Saying that he found the answer is just sad.

He's a liar
He didn't do anything. He just came up with a symbol for something he still can't do a freaking thing with anyway. All he did was save us the trouble of crashing some computers.

Dr. Alan U. Kennington
It's all very simple really. 0 divided by 0 is the solution of 0.x = 0, which is not unique. The solution is the set of all real numbers. You can't do much with this, but it is interesting to note that if you extend the real numbers by plus and minus infinity, you can say that 1/0 is the set of two numbers plus and minus infinity. But if you subtract these, you get, strangely enough, the set of all real numbers. Therefore 0/0 = infinity minus negative infinity. This is all very amusing at a primary/secondary school level (which is where I learned it in the 1960s), but all very trivial at the undergraduate uni level. Summary: the alleged "nullity" is none other than the set of all real numbers, as all mathematicians know.

Wait, he divided by zero OH SHI-

Garth Grant
We shan't recognize nullity here in California. Some concepts are too nutty even for us.

I still fail to see how this furthers the evolution of our species...

I dunno. I bet concept of 'zero' and imaginary numbers were jeered at then. This may be the case, but I just dunno.

Sågen-Hagénann Cromwellian
Anything divided by itself is 1. If you divide a pizza by 1, you have a pizza. If you divde a pizza by 0, you just didn't divide it, and you still have 1 pizza.

Johnny 99
Substituting the "number", nullity, for the word "undefined" brings us no closer to answering what it might mean to take the number zero to the zero-th power. Given the definitions provided in the film, the demonstration shows that the original expression can be easily translated into the penultimate one, yet the final step from zero divided by zero to the soultion, nullity, is not at all informative. We already knew our answer was not on the number line. That's why it's undefined. "Defining" nullity as a "number not on the number line" begs the question: what does "a number not on the number line" mean? Given that this 'discovery' is aimed at the problem of digitization, it seems t me that nullity is nothing moroe than an error trapping device. Kudos.

Something about this doesn't sound right. OK been a while since the my days or real analysis but here is my take. If you have one equation divided by another, if both equations tend to zero then eventually you will get 0/0, but different equations can give different results. e.g. 2x / x , as x goes to zero, you'd think well it is going to 0/0 but its obvious that 2x/x = 2 so the limit is a real number: 2. Then trivially take 3x/x, ok as x goes to zero then the end point (limit) looks like 0/0 but is in fact 3. So here we have two expressions that end up as 0/0 but give two different real results when looked at carefully. This is the kind of reasoning that has led mathematicians to say that zero divided by zero is meaningless. Interestingly, computers often determine this situation and give the value as NaN (not a number). But that is just used in error checking, so the pute can say "Error".

Ya right
Instead of demonstrating it to other maths professors or peers, he shows it to schoolkids. Add it to the long list of fake ass discoveries to get fame list.

computers should not be able to divide by zero, simply because it gives unexpected answers. Its actually much better if the computer throws an error, because you know its doing it wrong.

So 0/0 is nullity - big deal, now we have a label for it. What can you actually do with it? It isn't transitive, that's for damn sure.

Anything is possible. I'm worried that this might unravel time-space, though.

Chuck Norris
I mastered dividing by zero, -infinity years ago!!

Long Cat
My anwser may not be entirely right due to the fact that I only have a highschool level math. The problem I find with this is that Dr. Anderson's 'nullity' seems fairly reminiscent of Aleph-null. Which if I'm not mistaken represents all numbers.

cute trick, Anderson. Now what's (nullity)^(nullity)?

graham p
Logically anything divided by nothing still leaves you with the original thing, so I don't know why: n/0 != n ...just makes sense to me anyway.

Michael Burke
Lots of people have argued that this is utter nonsense, as if arithmetic really existed int he real world. Arithmetic (in fact, mathematics), is a set of tools we use to solve problems. (The number "4" for instance, does not exist except as a symbol to represent a conventional recognition of quantity.) We invented the tools, and sometimes they "don't make sense" but are useful anyway. Non-euclidean Geometry is an example of a tool that goes contrary to common sense. On a theoretical level, this "number" which is identified with the sets of infinite numbers, may have a real use. So what if it doesn't work on my slide rule yet.

Todd Allen Osterberg
This is the old Bill Clinton trick of redefining what the meaning of "is" is. If a student makes up an answer out of thin air it is called bunk. If a professor makes up an answer it is called "nullity". So, based upon the transitive property of numbers (if A=B and B=C then A=C), nullity is bunk.

Anonymous Panda
This is complete Garbage. In order for this theory, this man had to come up with a completely new number, a number that lies -outside- of the number line, therefore, it isn't even a feasible number. Once again, complete garbage.

James Dennett
So, nullity = 0/0. But then nullity = (2 x 0) / 0, which is 2 x (0/0), so nullity = 2 x nullity, so nullity = 0. Oh dear, this all fails to work. It's not that we don't know how to divide 0 by 0. It's that you can't come up with an answer without inviting all sorts of contradictions. The question is the problem. This trivial nonsense doesn't enable anything new in mathematics or computer science. It's the same kind of cheap parlour trick mathematicians have been using forever to "prove" that 1=0.

Vin Diesel
So much for "only six people in the universe."

a + b = c
I can't find the nullity button on my calculator.

Chuck Norris
Heck, I've known about this for years!

blank divided by zero is ...a symbol for zero divided by zero? Gee, that's brilliant! Oh, it's useless. Zero is not a removable discontinuity, it's a junction point between two number systems, and you're not going to get rid of the fact that it's not properly part of either (by design, or it would be useless) by making up a crappy symbol for it.

Does math need to get any harder than it is already?

Chuck Norris
I'm sorry people, but I'm the only one who can divide things into no groups. Many people could chop you in half, which is dividing you by 2. I once met a man who could chop you in half at the waist while simultaneously chopping you in half vertically. He divided you by 4. I've known some (few) ninja who could attack you, over time, such that the limit of the ninja's dividing power as ninja approaches you approached infinity. I don't wish to sound like I am arrogant, but have you ever met a ninja who could divide you into zero parts? I'm sorry, but the only other being capable of that, other than me, is God so I'm not going to let some professor think he can break the laws of physics.

var foo = 0 var bar = 10 if(foo){ bar / foo }

What the hell? Pacemakers don't have computers, so why would it suddenly decide to start doing math?

You fool.
"square root of -1 (another mathematical problem that creates errors)" - Jon The square root of -1 = "i"... It delves into complex numbers rather than just having a rational real number or a simple integer as the answer.

Can you divide longcat by nullity? dont think so.. If you cant, its completely useless to me...

Dr Anderson
4/4 = 1 3/3 = 1 2/2 = 1 1/1 = 1 0/0 = 1 It's that easy. BRILLIANT!

This is absolutely rediculous. Make up a new number because you're too lazy to work around the age old issue.

Rab Itchan
Nullity is all I think about every day. I sometimes cry myself to sleep thinking how it will never be acceptable mathematics.

Steve Hemingway
Well finished the first paper We expect a number system to behave in a way consistent with our world and nullity is 0 for must of us. Whilst dividing by 0 causes computing errors; we have consistent ways of processing these and the IEEE NaN (Not a Number), handles things the way we expect. Unfortunately Dr. Anderson create really worse problems as the axioms which split nullity and 0 would stop most computations being what we expect. I got as far as the first two of the 10 extra axioms. Sorry but if {null + a = null} and {-null = null} then a number 'a' equals either null or 0. Result more plane crashes. Anyway nice evening of reading, I must get back now to the more serious cold fusion experiments!

lol I can invent numbers too
lol if 3.14159... is Pi and x/0 is "nullity" then the square root of 2 is hereby known as "omegatron." Its symbol consists of many lines forming a snowflake inscribed in an irregular shape.

I'm hoping this is some sort of joke.... He didn't "solve" anything. Dividing by zero over the real numbers simply wasn't defined. You learn that you can make 0/0 or 0^0 equal anything, in a sense, in an introductory Calculus class! He didn't solve any "unsolved problem in math," he just redefined the real numbers. This wasn't even in an unsolved problem. This is kind of like saying, "I'm going to make a new number Z which is defined as a number that has the property Z + Z = Z. Now, I have 2Z = Z, so I divide by Z and solve the unsolved problem of how to make 2 = 1!"

Dan B.
The implications of teaching children that dividing by zero is possible, are absolutely terrifying. How can one expect to provide them with the mathematical background necessary to excel in higher education if your theory is to create numbers? When these children go out into the real world and are faced with real issues, how do you expect them to perform with this kind of background? If these children want to go into the sciences and mathematics, this is very poor preparation. They are in for a rude awakening.

When you divide zero by zero the answer is an undefined number because if x = 0\0 then x represent zero negative infinity positive infinity and all the numbers inbetween. The reason it does not equal anything is because there is no numerical value that can represent every number. This is an idiotic idea and nullity is not a number it's a variable that represents all numbers.

That's Numberwang!

"There are, however, contexts in which division by zero can be considered as defined. For example, division by zero z/0 for z in C^*!=0 in the extended complex plane C-* is defined to be a quantity known as complex infinity. This definition expresses the fact that, for z!=0, lim_(w->0)z/w==infty (i.e., complex infinity). However, even though the formal statement 1/0==infty is permitted in C-*, note that this does not mean that 1==0*infty. Zero does not have a multiplicative inverse under any circumstances." --Wolfram MathWorld I'd take established rules of calculus over this nonsense any day. Once again: "Zero does not have a multiplicative inverse under any circumstances."

to everyne who says it can no exist because you can't express it in binary, how do you express i in binary?

this guy solved the problem simply because he defined a solution to the problem that's like a student being asked what 0 - 1 is, and responding "booby" saying that "booby" is the result of subtracting one from zero there are no viable mathematical proofs, or applications for this "nullity"

If the brain is a computer surely watching the video will cause my head to explode.

The shame of Britain. They even got someone to publish the story. "Hey guys, no solution is now called nullity. GREATEST SCIENTIFIC BREAKTHROUGH EVER." All he did was give a special symbol to 0/0. He has not solve any problems. If I still cannot solve the famous 2 = 1 problem, then this man has done NOTHING. You need to divide by zero to prove 2 = 1.

Captain Obvious
You can't divide by zero! The Universe will implode!

I LIKED attempting to divide by 0.

This is profoundly stupid. They couldn't figure it out, so they gave their ignorance an official label and claimed it was the answer. It still doesn't give any kind of meaningful answer, and it has no practical application of any sort. This fails massively.

The Universe
I warned you guys not to divide by zero. Now you're gonna get swallowed by a black hole.

So...why spread the word in a high school and on TV? Shouldn't you be publishing in a paper somewhere? Get it down in writing where someone can give you credit for it, if they actually believe you.

Oh dear...
What's the first step in his derivation? 1/0 = infinity. He's used what he's trying to prove in his proof. Cyclic arguments are acceptable only as proof of contradiction, and only when the definition is proved wrong...

This should have been shown to degree and/or A level students, NOT junior schoolkids, who have a nasty tendancy to absorb whatever is thrown at them (we've all been there) Anybody can make up a name for a number, and im still fond of the 1/0 = infinity theory (although both sides of undefined, a dilemma indeed)

Waitaminnit is nullity ONLY 0/0 or would any other number work? Also, division by zero has always been possible, google the time dilation equation.

You know, math really IS easy if you simply decide that there's a new rule and start making stuff up from there. ...And why exactly would a pacemaker be forced to divide something by zero?

I understand what he is saying and it does work - in theory. But all he has proved is that we can make up imaginary numbers to solve problems that cannot be solved in real life but thats already been done before and when will this be of use? The day we discover the sixth dimension maybe.....

Prof. Richie McRichstonson
This is quite possibly the best mathematical solution ever found!

UK Anonymous
This can't be bloody right, there must be a mistake. It's not possible to divide by zero, it'd destroy the entire Earth.

Black Wyvern
That was complete mathematical herecy. The number line may not be a circle, that's just a piece of theory that didn't help solve the problem. IMO, solving this problem with reciprocals is a better idea. 1/x = a fraction close to zero. 1/infinity would be zero, theoretically. So we set up the reciprocal triange with that. .....1 ....----.. .0...|...Infinity From that we can see the relationship between 0, 1 and Infinity. 1/0 = Infinity This is a WAY better method than some stupid theory. Just so you know it works: .....2 ....----.. .3...|...2/3 2 divided by 3 = 2/3 3 x 2/3 = 2 2 divided by 2/3 = 3 Any 2 positive numbers should do that.

Steve Irwin
I divided by zero, and nullity didn't help me. AT ALL.

The problem with this "new number" that "[stretches] from negative infinity, through zero, to positive infinity," that will supposedly allow computers to grasp x/0, is that ANY equation can equal nullity. 1+1=nullity, 3*-3=nullity, etc. So unless you hard-code every programing language to only use this number in the event of dividing by zero, it will cause errors in any math problem. And then, say you have a flight computer, as the above article suggests, that needs to divide by zero, and then add 100, and that's how many yards it has left till it hits the ground. x/0+100=nullity, so it has anywhere between infinity and negative infinity until it crashes. That really narrows it down, huh? Now instead of the program getting syntax error, which will quit out of the program with an error message, the program gets a logical error, as it will attempt to manipulate a totally worthless number. What will the program assume? It's infinite miles away from the earth? It's infinite miles under the surface? Somewhere in between? The program wont crash, but the plane sure as hell will.

My mobile (SPV C600) does in fact devide by 0. It gives an answer of "0"

This is obviously a hoax, or something extremely stupid and irrelevant. How would you represent this in binary? Surely it's just algebraic. Is more like adding a word to the English language than solving a math problem.

Prof. Baker
any real number divided by zero does not exist. the pupils that have been taught this are now more stupid from being in dr anderson presence. this should never be taught in schools...EVER!

This must be hoax. No mathematician could say that this theory works or is usable. It is stated in the article that nullity is numbers from -infinity to +infinity but this is just not possible - infinity is not a number but an expression for any given amount of MORE numbers. So nullity cannot be defined as a number. This does not solve anything ether - all we could do is to change division by zero exception in our apps to nullity exception and still end up with the same solution.

Surely however as any number divided by itself is one this is also the same for zero and not nullity?!

Okay, I barly understand but what the hell are the doing!

IT MUST BE A HOAX. One of the clues is the mention of Pythagoras: he was around much before 1200 years ago, and as far as I remember, the ancient Greeks did not know zero!

Hubert J. again
Now that I watched the video, it's not even that! Heck, what I just said made more sense than that... What he wrote on the board: 0/0 = -0- (assuming true) 0^0 = 0^(1-1) = 0^1 * 0^-1 = 0/1 * 1/0 = 0/0 = -0- That's not a proof. That's just the same arbitrary definition he started with! "I assume that 0/0 is nullity. 0^0 is nullity. Therefore, nullity is a new number." No, it's still just 0/0. This is just a new funny symbol to say the same thing; Pythagoras, Fermat, and Riemann are rolling in their graves... laughing at this buffoon.

ha im in the front row. it was fun and we got to miss a lesson. yum

Thats just stupid. How does that help in any way? What are the properties of this made up value? How can you use them? Saying that dividing by 0 results in infinity is more useful than this. If I have ten apples and I divide them amongst zero people, each person gets how many apples? ZERO! Therefore anything / 0 = 0. Just stupid.

Mark W
There're plenty of books on infinity (not infinite mind you ;-) and they contain such definitions e.g. capitalised omega to represent infinity to the power infinity. This strikes me as more marketing than mathematics!

Pierre Keele
Dr Bedford would explode with anger if he saw this. Is this man a Dr of Philosophy and not Mathematics?! I see he is from the computer science department, has he never studied the laws, lemmas and definitions of Mathematics. You do not prove something by just inventing a new word.

0 to the power of 0 equals 1 (try it on your calculator). Therefore, nullity equals 1. QED

Everyone knows that when you divide by zero it's OVER NINE-THOUSAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAND Seriously, this is the most useless solution yet: instead of getting an error message you get nullity , which doesn't help more than the error message

Sounds like a hoax. Does not solve anything at all. If so, how do you write nullity in binary ???

Do I understand Dr Anderson's theory? Not a word


Sounds interesting. Too bad the videos are in Real Player which ruins your computer worse than diving by zero so i won't watch them.

Prof. Hubert J. Farnsworth
All he did is give a name to the opposite pole of a non-Euclidean, spherical geometry. He tied the two "ends" of the number line together to make a loop. And I'm fairly sure non-Euclidean geometry is not new.

Pity the downloads don't work.

This is absolutely ridiculous. Dividing by zero is completely unnecessary AND impossible. It can't be imagined (as a root of -1 can).

i hope i am not wrong, but my understanding is that basically he is telling people to see the number 0, not as a number but as a concept of nothingness in which case, i do see computers and aplications benefit from it, in the logicla sens eof which computers work at the moment, when they come up to divide by zero they fail becuase that is how we have always programed them to be but if we now tell the computer 0 is not a number of value, but a variable of the concept nothingness, then we could over come many situations when we coudl formulate and have variables of no use or no avaliability.. the thing is, computer would eb able to "rationalize" on the 0 divisions, becuase they would treat the variable as a non existant of data, and still carry on the procces, instead of looping out in error... do i make sense? o.O

Mitchell H.
Ryan, whatever you're on, I want some of it.

Black holes, everywhere. Nice job, Dr. Anderson.

CANNOT DIVIDE BY ZERO!!!!!111oneoneone

So, what? He just made up a new number because he got frustrated not being able to work it out?

Thomas Chapman
He has not 'solved' anything - he has just given an existing result a name. This won't 'fix' a flight computer either - it doesn't change anything.

I propose a new number based on this nullity breakthrough: infinullity. Infinullity is the number that results when one divides infinity by zero. I anticipate that it will be just as useful as nullity itself. Seriously though, I don't know much about pacemakers or autopilot algorithms, but if either actually performs division, one would think it would include some form of exception handling for the case of dividing by zero already.

Chris Croughton
I feel sorry for those children when they find out that computers have been happily handling such operations for decades. The value NaN ("Not a Number") is generated by exactly that kind of invalid operation, like zero raised to the power zero. It even comes in both positive and negative forms! And computers happily handle the results of using it in subsequent calculations, and will generate traps so that the error can be automatically corrected (and so don't crash and "fail to start in the morning" like his car example).

George Bush
This is absurd, you can't just take two unknown quantities and set them to your own made up definition. I would like to see this "genius" come up with a way for this magical number to be represented in binary

What has science done?

Patrick Bampton
What is a RAM auto file? Why not present the explanations in html or pdf format. Then I might be able to read them.

calling 0/0 nullity gives you nothing, its by far not as smart as calling sqrt(-1)=i... they have to show how to do some (new!!!) maths with it.

his biggest mistake is assuming 1/0 is infinity and -1/0 is negitive infinity, which it is not, its its own seperate entity. 1/0 is essentially unitless much in the way zero is

Peter H
Dr. Anderson claims that 1/0 = infinity -1/0 = negative infinity 0/0 = nullity 0/0 = (0/1) * (1/0) = 0 * infinity = nullity so 0 * infinity = nullity, right? But, if 1/0 = infinity, then it stands that infinity * 0 = 1 thus 1 = nullity? I fail to see how this idea could withstand basic algebra.

Chris Croughton
That 'theory' is total rubbish. All he has done is replace "zero divided by zero is indeterminate" (it can be anything from zero to infinity, depending on how it is derived) but "I'm going to use this symbol for it", which doesn't alter anything. He didn't "solve the problem", he merely said "I'm going to call the answer 'nullity'" and trivially dismissed the actual problem (which is that "zero divided by zero" is as meaningless as "this statement is false").

It's a great idea, but he shouldn't get credit for "discovering" something.... if i where to make up a symbol for the square root of -1 (another mathematical problem that creates errors) should I get some kind of global recognition for my genius? no, it's just a form of shorthand or short cut. nothing great. -Jon

Captain Homo
the idea of 0/0= -0- (or however it would look) is stupid. if we have (0*x)/0 = (0*5)/0 0/0 * x = 5 * 0/0 then -0- * x = 5 * -0- | : -0- x=5 but in reality that just doesn't work.

O.O Devision by zero IS possible!

divide anything by nothing, you'll still have nothing divised, so, no changes. marons.

Atif Hassan
Its good. But I think there is nothing new or special about it. Its obvious. but what problem has been solved? infinity is always there.

I thought of that number months ago and have come up with an unconventional "number circle" to help explain it better. This was a short text file i created a while back to explain it: "The "Number Line" that we all learned in school in not actually a line, but a circle. The top of the circle is 1, the bottom of the circle is -1, the right side of the circle is 0, and the left side of the circle is a number we have yet to define. This number is the number right between negative infinity and infinity, but on the opposite side of the circle as 0. The circle is set up so that the negative of any positive number is on the exact opposite side of the circle over the horizontal axis and the inverse of any number is on the opposite side of the circle over the vertical axis. This means that 0 which can be written as 0/1 has an inverse over the vertical axis of the undefined number which can be written as 1/0. Anytime in calculus when you get a vertical asymptote, it is actually equal to the undefined value 1/0. This means that the expression 1/0 does indeed exist, but has yet to be defined by modern mathematics."

Robin Andersson
Dr Anderson have not solved anything, just ignored it. Making a new number out of nowhere doesn't make it real.

Jimmy Hamilton-Brown
I think I understand it - but I am not sure what we have gained apart from a new symbol which is not on my computer - come to think of it nor is infinity!

unfortuanately i could not view it on the internet, i think from what i saw on the tv, was quite impressive.

a new number? AMAZING!

R Page
Dr Anderson's theory is explained well, but it would more useful if the film allowed viewers to see what he was writing on the board.

John Nolan
So if my new pacemaker divides by zero, I won't die? How will that work then? I've watched the prof's video, but can't quite work that one out...

in the derivation when the expression 1/0 x 0/1 is written isn't the 1/0 undefined and the solution unattainable?

Ooh, I just saw this on the news, and :o oo strange.

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