PS. and of course there is THE example of finite verses INFINITE, the twin prime problem. Query. Is there an easily described sequence which has been PROVED to be finite but we don't know what the last term is? At 03:11 AM 10/27/2007, you wrote:
I strongly second Phil's suggestion. The mathematical world didn't have to wait for Cantor to deal with infinity. Euclid and co. knew exactly what they were saying about the prime numbers and so would the average radio listener. You can get quite a bit of mileage out of this area. After describing Euclid's PROOF it's natural to think about possible primality for Fermat and Mersenne numbers. You can tell lots of interesting stories, how Euler factored F5, current results about finding large Mersenne's and factoring large Fermat's the intriguing fact that there are probably INFINITELLY many M's but only a finite number of F's, -we may know them all already. I would stay away from Cantorian infinity, much as we love it. People, as opposed to mathematicians, find it hard to digest and it really doesn't play a role in most of the rest of mathematics.
DG
From: James Propp <jpropp@cs.uml.edu>
I've been invited to speak on a college morning radio program next week, on the topic of mathematical proof and infinity. It'll be a conversation with two interviewers (no call-ins).
I've not notice anyone mention proofs of the infinitude of primes yet. That should be simple enough for anyone reasonably awake to understand, and introduces both important techniques used in mathematical proof as well as an infinity.
Phil
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