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:
\forall a \in X,\ a R a
For example, "is greater than or equal to" is a reflexive relation but "is greater than" is not. 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
\forall a \in X,\ a = a
is called the axiom of equality in some systems.

 

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