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Song Li

@brandonsongli.bsky.social

17 followers 65 following 0 posts

If I were to take the best response that sustains this equilibrium, I would be complicit.

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Tien Chih

@tienchihmath.bsky.social

So THIS is the best line I've seen in a proof.

Vince Vatter @vatter.bsky.social · Jan 22

Contrapositives are for cowards. Behold.

$Theorem. If $n$ is an integer and $n^2$ is even, then $n$ is itself even. Proof. Contrapositives are for cowards, so assume $n$ is an integer and $n^2$ is even. Then $n^2=2k$ for some integer $k$, and thus $n^2-2k=0$. Behold: \[ n = n + (n^2-2k) = n(n+1)-2k. \] Both $n(n+1)$ and $2k$ are even, so $n$ is even. QED.$

January 22, 2025 at 6:14 PM