Definition 1. A binary relation $\sim$ on a set $X$ is well-founded if every non-empty subset $A \subseteq X$ has a $\sim$-minimal element, i.e. an element $a \in A$ such that
\[\forall x \in A : x \not\sim a.\]References
- [1]
- Wikipedia contributors. Well-founded relation. Wikipedia, The Free Encyclopedia.
- [2]
- Thomas Jech. Set Theory. 3rd Millennium ed, rev. and expanded. Springer, 2002. p. 25.