# Definition:Inverse Mapping/Also defined as

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## Definition

Let $f: S \to T$ be an injection.

Then its **inverse mapping** is the mapping $g$ such that:

- $(1): \quad$ its domain $\Dom g$ equals the image $\Img f$ of $f$
- $(2): \quad \forall y \in \Img f: \map f {\map g y} = y$

Thus $f$ is seen to be a surjection by tacit use of Restriction of Mapping to Image is Surjection.

$\mathsf{Pr} \infty \mathsf{fWiki}$ does not endorse this approach, and considers that its use can cause important insight to be missed.

## Also see

- Results about
**inverse mappings**can be found here.

## Sources

- 1999: András Hajnal and Peter Hamburger:
*Set Theory*... (previous) ... (next): $1$. Notation, Conventions: $10$