Category:Examples of Well-Founded Relations

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This category contains examples of Well-Founded Relation.

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.

Pages in category "Examples of Well-Founded Relations"

The following 2 pages are in this category, out of 2 total.