Wikipedia:Reference desk/Archives/Mathematics/2011 August 1

= August 1 =

Aleph and beth numbers
Why did they choose Hebrew letters to represent these values instead of Greek letters? --134.10.116.13 (talk) 21:24, 1 August 2011 (UTC)
 * "They" would be Georg Cantor (at least for the aleph; I'm not sure the beth wasn't a later extrapolation using the same pattern). I don't believe he ever said precisely why.  There are those who think it's related to his supposed Jewish origin, and I suppose that's possible, but there is no proof of that (it is clear that he was Christian as a matter of religion).
 * Practically speaking, though, most of the Greek letters were already spoken for, often several times, so it was really a pretty good idea. --Trovatore (talk) 21:32, 1 August 2011 (UTC)
 * Who knows after this time but he had some ideas about identifying infinity with God and he might have chosen aleph because of its associations this way. Dmcq (talk) 21:46, 1 August 2011 (UTC)
 * What associations does aleph have with god? Algebraist 21:53, 1 August 2011 (UTC)
 * Just stick 'aleph god' into google and you get more than you could ever possibly want on people getting mystical. Dmcq (talk) 22:04, 1 August 2011 (UTC)
 * Ommmm.... 64.134.228.55 (talk) 01:40, 2 August 2011 (UTC)

An inequality
Given a, b, c, all >0 and a+2b+c=1, prove that (or find counterexample to)
 * $$a \log a + 2 b \log b + c \log c \ge 2[(a+b) \log (a+b) + (b+c) \log (b+c)]$$

with equality iff b2=ac. (This compares the entropy rate for a two state Markov chain with the entropy rate for a random bit stream with the same distribution.) I had an idea to use the concavity of the function plogp but I couldn't get it to work. I have one or two other ideas but they will probably get messy, so I'm wondering if there is a neat trick that can be used.--RDBury (talk) 23:03, 1 August 2011 (UTC)
 * Never mind, I got the concavity idea to work.--RDBury (talk) 23:43, 1 August 2011 (UTC)