Definition:Reflexivity

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Definition

Let $\RR \subseteq S \times S$ be a relation in $S$.


Reflexive

$\RR$ is reflexive if and only if:

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


Coreflexive

$\RR$ is coreflexive if and only if:

$\forall x, y \in S: \tuple {x, y} \in \RR \implies x = y$


Antireflexive

$\RR$ is antireflexive if and only if:

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


Non-reflexive

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


Also see

  • Results about reflexivity of relations can be found here.