Definition:Irreflexive Relation

Disambiguation

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Irreflexive Relation may refer to:

Antireflexive Relation

$\RR$ is antireflexive if and only if:

$\forall x \in S: \tuple {x, x} \notin \RR$

Non-Reflexive Relation

$\RR$ is non-reflexive if and only if it is neither reflexive nor antireflexive.

Also defined as

Some sources define an irreflexive relation to be a relation which is not reflexive.

Hence, under such a definition, an antireflexive relation would also be classified as an irreflexive relation.

Because of such ambiguity of usage, the term irreflexive relation is deprecated on $\mathsf{Pr} \infty \mathsf{fWiki}$.