Well-ordering principle: Every nonempty subset S⊆NS\subseteq\mathbb{N} has a least element (with respect to the usual order on N\mathbb{N}); that is, there exists m∈Sm\in S such that m≤sm\le s for all s∈Ss\in S.

Remarks

This is exactly the statement that (N,≤)(\mathbb{N},\le) is a . It is equivalent in strength (over standard basic assumptions) to .