Reflexive - Definition and Overview

In 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:

<math>\forall a \in X,\ a R a<math>

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

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.