Proof of mathematical induction: Difference between revisions

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Converse: adjusted section on converse in light of addition of (A2)
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==Converse==
Conversely, the axiom (A1) can be proved by the principle of [[mathematical induction]]. Indeed, given (A2), the two are equivalent.
 
Let ''S'' be a set of natural numbers. We want to prove that if ''S'' has no smallest element then ''S'' is empty.