Back at the uni, I was shown a nice proof that one infinity (the (infinite) count of natural numbers) is not the same as another infinity (the count of real num

Back at the uni, I was shown a nice proof that one infinity (the (infinite) count of natural numbers) is not the same as another infinity (the count of real numbers, IIRC). Basically, it was shown no mathematical function can be constructed that maps one onto another, IIRC. Also, please note the Cantor's theorem [0] -- this bears some relation to programming, as considering subsets of a set is an important problem. In short, it makes sense to discuss different infinities. All that may sound purely academic theory, but please remember current cryptography grew from what once seemed to be just purely academic theory. ---- [0] http://en.wikipedia.org/wiki/Cantor_theorem http://en.wikipedia.org/wiki/Cantor_theorem