Reflexivity

Definition: Reflexive Relation

A relation $R\subseteq A\times A$ is reflexive iff

$$xRx$$

is true for all $x\in A$.

Definition: Irreflexive Relation

A relation $R\subseteq A\times A$ is irreflexive if there is no $x\in A$ such that

$$xRx$$

NOTE

Irreflexive relations are also called anti-reflexive or aliorelative.