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ulfarsson.bsky.social
@ulfarsson.bsky.social
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vatter.bsky.social
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 5:58 PM