Category:Well-Founded Relations

This category contains results about Well-Founded Relations.
Definitions specific to this category can be found in Definitions/Well-Founded Relations.

Definition 1

$\RR$ is a well-founded relation on $S$ if and only if:

$\forall T \subseteq S: T \ne \O: \exists z \in T: \forall y \in T \setminus \set z: \tuple {y, z} \notin \RR$

where $\O$ is the empty set.

Definition 2

$\RR$ is a well-founded relation on $S$ if and only if:

for every non-empty subset $T$ of $S$, $T$ has a minimal element.