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
\[\forall x \in A : x \not\sim a.\]
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
\[\forall x \in A : x \not\sim a.\]