Definition:Reflexive Closure/Intersection of Reflexive Supersets

Definition
Let $\mathcal R$ be a relation on a set $S$.

Let $\mathcal Q$ be the set of all reflexive relations on $S$ that contain $\mathcal R$.

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


 * $\mathcal R^= := \bigcap \mathcal Q$

That is:


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

Also see

 * Equivalence of Definitions of Reflexive Closure