# Reflexive relation

In mathematics, a homogeneous binary relation *R* on a set *X* is **reflexive** if it relates every element of *X* to itself.^{[1]}^{[2]}

An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to have the **reflexive property** or is said to possess **reflexivity**. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations.

An example of a coreflexive relation is the relation on integers in which each odd number is related to itself and there are no other relations. The equality relation is the only example of a both reflexive and coreflexive relation, and any coreflexive relation is a subset of the identity relation. The union of a coreflexive relation and a transitive relation on the same set is always transitive.

Authors in philosophical logic often use different terminology.
Reflexive relations in the mathematical sense are called **totally reflexive** in philosophical logic, and quasi-reflexive relations are called **reflexive**.^{[7]}^{[8]}