Definition:Diagonal Relation

Definition
Let $S$ be a set.

The diagonal relation on $S$ is a relation on $S$ such that:


 * $\Delta_S = \left\{{\left({x, x}\right): x \in S}\right\} \subseteq S \times S$

This is sometimes called the equality relation.

It is also referred to it as the diagonal set or diagonal subset, but it can be useful to retain the emphasis that it is indeed a relation.

Also see
Note that the diagonal relation on $S$ is the same as the identity mapping $I_S$ on $S$.