# well-founded

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.

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- [MLA] “well-founded.”
*Platonic Realms Interactive Mathematics Encyclopedia.*Platonic Realms, 10 Apr 2014. Web. 8 Oct 2015. <http://platonicrealms.com/> - [APA] well-founded (10 Apr 2014). Retrieved 8 Oct 2015 from the
*Platonic Realms Interactive Mathematics Encyclopedia:*http://platonicrealms.com/encyclopedia/well-founded/