Definition:Reflexive Closure/Union with Diagonal

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

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


 * $\RR^= := \RR \cup \set {\tuple {x, x}: x \in S}$

That is:


 * $\RR^= := \RR \cup \Delta_S$

where $\Delta_S$ is the diagonal relation on $S$.

Also see

 * Equivalence of Definitions of Reflexive Closure