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:
A relation that is not reflexive is irreflexive. For example, "is greater than or equal to" is a reflexive relation but "is greater than" is irreflexive. Other examples of reflexive relations include: "is equal to" (equality) "is a subset of" (set inclusion) "is less than or equal to" and "is greater than or equal to" (inequality) "divides" (divisibility) 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
:
is called the axiom of equality in some systems.
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