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

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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)

$a\log a+2b\log b+c\log c\ge 2[(a+b)\log (a+b)+(b+c)\log (b+c)]$

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)