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

In notation, this is:

For example, "is greater than or equal to" is a reflexive relation but "is greater than" is not.

Examples of transitive 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.

Set theory

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