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Could someone provide a wrong clime and its wrong proof by induction so that only the first step be wrong?

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For all $n \in \Bbb N$, show that $n > n+1$. Skip step $1$ and assume that for $n \geq 2$, that $n > n+1$. Then let $n = k+1$, whence $(k+1) + 1 < (k) + 1 = k+1$, clearly wrong.

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