Cantor's Diagonalization

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.