Definition:Antireflexive Relation

Definition

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

$\mathcal R$ is antireflexive iff:

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

Also known as

Some sources use the term irreflexive.

Also see

• Reflexivity of Relations

• Reflexive Relation
• Coreflexive Relation
• Non-reflexive Relation

• Results about reflexivity of relations can be found here.

Sources

• Steven A. Gaal: Point Set Topology (1964)... (previous)... (next): Introduction to Set Theory: $1$. Elementary Operations on Sets
• Gary Chartrand: Introductory Graph Theory (1977): Appendix $\text{A}.2$