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.
- [MLA] “well-ordered.” Platonic Realms Interactive Mathematics Encyclopedia. Platonic Realms, 10 Apr 2014. Web. 19 Dec 2018. <http://platonicrealms.com/>
- [APA] well-ordered (10 Apr 2014). Retrieved 19 Dec 2018 from the Platonic Realms Interactive Mathematics Encyclopedia: http://platonicrealms.com/encyclopedia/well-ordered/