Definition:Non-Reflexive Relation

Definition
Let $\RR \subseteq S \times S$ be a relation in $S$. $\RR$ is non-reflexive it is neither reflexive nor antireflexive.

Also defined as
Some sources define a non-reflexive relation to be a relation which is not reflexive.

Hence, under such a definition, an antireflexive relation would count as being a non-reflexive relation.

Also known as
Some sources use the term irreflexive.

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

Also see

 * Definition:Reflexivity


 * Definition:Reflexive Relation
 * Definition:Coreflexive Relation
 * Definition:Antireflexive Relation