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Cantor's Diagonalization
- mojoe 7y agoThis is my favorite math proof. I'd love to hear yours!
- ColinWright 7y agoI prefer Cantor's first proof of the uncountability of the reals to the diagonalisation argument. Perhaps my favourite proof is this: As a continued fraction, 1+sqrt(2) = [2;2,2,2,2,...]. Hence sqrt(2) is irrational. A close second is this: Let n be an integer with n>2. Consider 2^(1/n). If this is rational then 2^(1/n) = a/b. Hence 2b^n=a^n, which we can write as b^n+b^n=a^n. By Fermat's Last Theorem that has no solutions in integers, hence 2^(1/n) is irrational. But my choice of favourite proof varies from week to week.