Definition:Image (Set Theory)/Mapping/Mapping/Definition 2

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Definition

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

$\Img f = f \sqbrk S$

where $f \sqbrk S$ is the image of $S$ under $f$.


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 $\image f$ 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.


Also see


Sources