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.

However, as irreflexive is also found in other sources to mean non-reflexive, it is better to use the clumsier, but less ambiguous, antireflexive.

Also see

 * Definition:Reflexivity


 * Definition:Reflexive Relation
 * Definition:Coreflexive Relation
 * Definition:Non-reflexive Relation