Definition:Diagonal Relation

Definition
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:


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

Also see

 * Definition:Equals
 * Diagonal Relation is Equivalence


 * Definition:Identity Mapping