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Prove that $n \ne n+1 $ for all $ n \in \mathbb N.$

How do I prove this statement using only Peano axioms?

Henry
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Twilight
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  • See here: https://math.stackexchange.com/questions/1671154/how-to-prove-that-doesnt-exist-a-natural-number-such-that-is-equal-to-it-success – 79037662 Oct 17 '19 at 16:57

1 Answers1

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You'll have to use induction. Here is a formal proof in Fitch, which has Induction as a built in rule. Note that $s(x)$ is the successor function, i.e. $s(x)=x+1$

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Bram28
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