# Category:Definitions/Inverse Mappings

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This category contains definitions related to Inverse Mappings.

Related results can be found in Category:Inverse Mappings.

Let $S$ and $T$ be sets.

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

Let $f^{-1} \subseteq T \times S$ be the inverse of $f$:

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

Let $f^{-1}$ itself be a mapping:

- $\forall y \in T: \tuple {y, x_1} \in f^{-1} \land \tuple {y, x_2} \in f^{-1} \implies x_1 = x_2$

and

- $\forall y \in T: \exists x \in S: \tuple {y, x} \in f$

Then $f^{-1}$ is called the **inverse mapping of $f$**.

## Pages in category "Definitions/Inverse Mappings"

The following 4 pages are in this category, out of 4 total.