# Reflexive relation

In logic and mathematics, a binary relation R over a set X is reflexive if for all a in X, a is related to itself.

In mathematical notation, this is:

[itex]\forall a \in X,\ a R a[itex]

A relation that is not reflexive is irreflexive or aliorelative.

For example, "is greater than or equal to" is a reflexive relation but "is greater than" is irreflexive.

Other examples of reflexive relations include:

A reflexive relation that is also transitive is a preorder. A preorder that is antisymmetric is a partial order. A preorder that is symmetric is an equivalence relation.

The statement

[itex]\forall a \in X,\ a = a[itex]

is called the axiom of equality in some systems.de:Reflexivität es:Relacin reflexiva pl:Relacja zwrotna zh:自反关系

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