well-ordering principle for natural numbersWellOrderingPrinciple2001-10-16 08:37:552007-06-23 16:58:26Axiom\usepackage{amssymb}
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Every nonempty set $S$ of natural numbers contains a least element; that is, there is some number $a$ in $S$ such that $a \leq b$ for all $b$ belonging to $S$.\\
Beware that there is another statement (which is equivalent to the axiom of choice) called the \emph{well-ordering principle}. It asserts that every set can be well-ordered.
Note that the well-ordering principle for natural numbers is equivalent to the principle of mathematical induction (or, the principle of finite induction).