well-ordering principle for natural numbers
Every nonempty set of natural numbers![]()
contains a least element; that is, there is some number in such that for all belonging to .
Beware that there is another statement (which is equivalent![]()
to the axiom of choice
![]()
) called the 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).