Definition:Well-Founded Relation/Definition 1

Definition
Let $\struct {S, \RR}$ be a relational structure. $\RR$ is a well-founded relation on $S$ :
 * $\forall T \subseteq S: T \ne \O: \exists z \in T: \forall y \in T \setminus \set z: \tuple {y, z} \notin \RR$

where $\O$ is the empty set.

That is, $\RR$ is a strictly well-founded relation on $S$ :
 * for every non-empty subset $T$ of $S$, there exists an element $z$ in $T$ such that for all $y \in T \setminus \set z$, it is not the case that $y \mathrel \RR z$.

Also see

 * Equivalence of Definitions of Well-Founded Relation