
Cantor's Diagonalization - mojoe
https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument
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mojoe
This is my favorite math proof. I'd love to hear yours!

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ColinWright
I 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.

