# Symbols:Greek/Delta/Diagonal Relation

## Diagonal Relation

$\Delta_S$

Let $S$ be a set.

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

$\Delta_S = \set {\tuple {x, x}: x \in S} \subseteq S \times S$

Alternatively:

$\Delta_S = \set {\tuple {x, y}: x, y \in S: x = y}$

The $\LaTeX$ code for $\Delta_S$ is \Delta_S .