Definition:Diagonal Relation

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

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

This is sometimes called the equality relation and denoted $$I_S$$.

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.