Definition:Coreflexive Relation

From ProofWiki
Jump to navigation Jump to search

Definition

Let $\mathcal R \subseteq S \times S$ be a relation in $S$.

Definition 1

$\mathcal R$ is coreflexive if and only if:

$\forall x, y \in S: \left({x, y}\right) \in \mathcal R \implies x = y$


Definition 2

$\mathcal R$ is coreflexive if and only if:

$\mathcal R \subseteq \Delta_S$

where $\Delta_S$ is the diagonal relation.


Linguistic Note

Coreflexive is pronounced co-reflexive, not core-flexive.


Also see

  • Results about reflexivity of relations can be found here.