Favorite Math Result

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What is your favorite math result/theorem?

Mine is the Tweedledum and Tweedledee principle from Winning Ways for your Mathematical Plays by Conway, Berlekamp, and Guy. Informally, it says that any partizan combinatorial game has a value of zero if the players can swap moves and the game is still worth the same value.

I like the proof that there is no limit to the number of consecutive integers there are without a prime.

That is, for any N, find integers i, i+1, i+2, ..., i+N-1 such that none of the integers are prime.

The best part about it is that many people who aren't mathematicians can often understand it.

All numbers (integers) are interesting.

If they weren't then there is a smallest non interesting number. Which makes it interesting.

More seriously.....

If you randomly permute N objects the expected number to remain unmoved is 1.
I might have expected it to vary as N changed.

QED