Definition:Reflexive Closure/Intersection of Reflexive Supersets

Definition
Let $\RR$ be a relation on a set $S$.

Let $\QQ$ be the set of all reflexive relations on $S$ that contain $\RR$.

The reflexive closure of $\RR$ is denoted $\RR^=$, and is defined as:


 * $\RR^= := \bigcap \QQ$

That is:


 * $\RR^=$ is the intersection of all reflexive relations on $S$ containing $\RR$.

Also see

 * Equivalence of Definitions of Reflexive Closure