Could someone provide a wrong clime and its wrong proof by induction so that only the first step be wrong?
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1[All horses are the same color](https://en.wikipedia.org/wiki/All_horses_are_the_same_color). – JMoravitz Oct 23 '17 at 04:59
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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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