A set with a partial order defined on its elements is said to be well-founded if for every subset there is a minimal element under the relation. If the order relation on the set is a total order then this condition is equivalent to it being well-ordered.

For example, any group of people ordered by their age in years is well-founded, since there will always be at least one person not older than anyone else in the group.

Citation Info

  • [MLA] “well-founded.” Platonic Realms Interactive Mathematics Encyclopedia. Platonic Realms, 10 Apr 2014. Web. 17 Feb 2019. <>
  • [APA] well-founded (10 Apr 2014). Retrieved 17 Feb 2019 from the Platonic Realms Interactive Mathematics Encyclopedia:


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