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# 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.

Citation Info

• [MLA] “well-ordered.” Platonic Realms Interactive Mathematics Encyclopedia. Platonic Realms, 10 Apr 2014. Web. 20 Nov 2018. <http://platonicrealms.com/>
• [APA] well-ordered (10 Apr 2014). Retrieved 20 Nov 2018 from the Platonic Realms Interactive Mathematics Encyclopedia: http://platonicrealms.com/encyclopedia/well-ordered/