= Well-ordering principle for the natural numbers
{title2=$S\subseteq\mathbb N,\ S\ne\varnothing\Rightarrow\min S\text{ exists}$}
= Well-ordering principle
{synonym}
Every nonempty subset of the <natural numbers> has a least element in their usual order. Applying this principle to positive integer linear combinations proves <Bézout's identity>. This principle for the usual natural-number order is distinct from the general <well-ordering theorem> asserting that every set can be equipped with some well-order.
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