# Category:Identity Mappings

This category contains results about Identity Mappings.

The identity mapping of a set $S$ is the mapping $I_S: S \to S$ defined as:

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

or alternatively:

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

That is:

$I_S: S \to S: \forall x \in S: \map {I_S} x = x$