# Definition:Image of Mapping/Definition 1

## Definition

The image of a mapping $f: S \to T$ is the set:

$\Img f = \set {t \in T: \exists s \in S: \map f s = t}$

That is, it is the set of values taken by $f$.

## Also presented as

The image of a mapping $f: S \to T$ can also be presented in the form:

$\Img f = \set {\map f s \in T: s \in S}$

## Also denoted as

The notation $\Img f$ to denote the image of a mapping $f$ is specific to $\mathsf{Pr} \infty \mathsf{fWiki}$.

The usual notation is $\map {\mathrm {Im} } f$ or a variant, but this is too easily confused with $\map \Im z$, the imaginary part of a complex number.

Hence the non-standard usage $\Img f$.

Some sources use $f \sqbrk S$, where $S$ is the domain of $f$.

Others just use $\map f S$, but that notation is deprecated on $\mathsf{Pr} \infty \mathsf{fWiki}$ so as not to confuse it with the notation for the image of an element.

## Technical Note

The $\LaTeX$ code for $\Img {f}$ is \Img {f} .

When the argument is a single character, it is usual to omit the braces:

\Img f