Definition:Reflexive Closure/Union with Diagonal

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

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


 * $\mathcal R^= := \mathcal R \cup \left\{{\left({x, x}\right): x \in S}\right\}$

That is:


 * $\mathcal R^= := \mathcal R \cup \Delta_S$

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