# well-ordered

A set with a total ordering defined on its elements is said to be *well-ordered* if every non-empty subset contains a least element under the relation.

For example, the set of natural numbers is well-ordered by the less-than (<) relation, but the set of integers is not well-ordered by < because it has no least element.

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- [MLA] “well-ordered.”
*Platonic Realms Interactive Mathematics Encyclopedia.*Platonic Realms, 10 Apr 2014. Web. 18 Nov 2017. <http://platonicrealms.com/> - [APA] well-ordered (10 Apr 2014). Retrieved 18 Nov 2017 from the
*Platonic Realms Interactive Mathematics Encyclopedia:*http://platonicrealms.com/encyclopedia/well-ordered/