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. 17 Feb 2019. <>
  • [APA] well-ordered (10 Apr 2014). Retrieved 17 Feb 2019 from the Platonic Realms Interactive Mathematics Encyclopedia:


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