Category:Definitions/Inverses of Mappings

This category contains definitions related to Inverses of Mappings.
Related results can be found in Category:Inverses of Mappings.

Let $f: S \to T$ be a mapping.

The inverse of $f$ is its inverse relation, defined as:

$f^{-1} := \set {\tuple {t, s}: \map f s = t}$

That is:

$f^{-1} := \set {\tuple {t, s}: \tuple {s, t} \in f}$

That is, $f^{-1} \subseteq T \times S$ is the relation which satisfies:

$\forall s \in S: \forall t \in T: \tuple {t, s} \in f^{-1} \iff \tuple {s, t} \in f$