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.