\begin{definition}[Definition:Reflexive Closure/Union with Diagonal]
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 $S$.
\end{definition}