Reflexive closure

In mathematics, the reflexive closure of a binary relation on a set is the smallest reflexive relation on that contains, i.e. the set.
For example, if is a set of distinct numbers and means " is less than ", then the reflexive closure of is the relation " is less than or equal

Definition

The reflexive closure of a relation on a set is given by
In plain English, the reflexive closure of is the union of with the identity relation on

Example

As an example, if
then the relation is already reflexive by itself, so it does not differ from its reflexive closure.
However, if any of the reflexive pairs in was absent, it would be inserted for the reflexive closure.
For example, if on the same set
then the reflexive closure is