Category:Definitions/Diagonal Relation

This category contains definitions related to Diagonal Relation.
Related results can be found in Category:Diagonal Relation.

Let $S$ be a set.

The diagonal relation on $S$ is the relation $\Delta_S$ on $S$ defined as:

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

Alternatively:

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