Posted Apr 16, 2004 by manolan
Gnomon,
You refer to 'Alf, but then when you introduce the Western Greek alphabet, you refer to Aleph for the first time. Also, I had always thought it was aleph, beth, etc. Are there two traditions of naming the phoenician alphabet, or is that something different altogether?
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Posted Apr 16, 2004 by Gnomon [See A60420098 for details of new sign-in system]
You're right! I slipped up. I'll get the eds to change the one use of Aleph to 'Alf.
There are two traditions of naming the Phoenician letters. The original names of the letters were never recorded, but the names of the Hebrew letters were written down (in the Bible) many centuries later. Some scholars have "reconstructed" the original names from the very similar names used in Greek, Hebrew and Arabic. I've used these conjectural names in the entry.
Many people just use the Hebrew names, because the Hebrew alphabet conveniently has exactly the same 22 letters as the Phoenician, although some of their uses have changed. Aleph is the Hebrew name, which I started out using before I discovered the reconstructed names.
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Posted Dec 26, 2006 by MrKeen
Aleph is also uused to designate cardinality of transfinite numbers: aleph 1 is cardinal number of denumerable transfinite (eg. natural numbers or any set thatcan be put into a one y=to one correspondence with natural numbers), while aleph 2, 3... designate non-denumerable transfinite numbers (aleph 2 is the cardinal number for the set of rational numbers.
Is thre any relatioship between this use of 'aleph' and Phoenician?
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Posted Dec 27, 2006 by Gnomon [See A60420098 for details of new sign-in system]
That Aleph was just chosen because it is the first letter of the Hebrew alphabet.
I believe Aleph subscript 0 is the infinity which enumerates the natural numbers and rational numbers. The guy who invented them (perhaps Cantor) discovered that the number which enumerates real numbers is bigger (in a certain meaning of the word), but he didn't want to call it Aleph subscript 1, because there might be another infinite number in between, so he called it C (from the first letter of Continuum). So his planned series of Aleph 0, Aleph 1 etc never got beyond the first of them.
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