Definition:Mapping/Diagrammatic Presentations/Infinite

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Diagrammatic Presentation of Mapping on Infinite Set

The following diagram illustrates the mapping:

$f: S \to T$

where $S$ and $T$ are areas of the the plane, each containing an infinite number of points.


$\Dom f$ is the domain of $f$.
$\Cdm f$ is the codomain of $f$.
$\Img f$ is the image of $f$.

Note that by Image is Subset of Codomain:

$\Img f \subseteq \Cdm f$

There are no other such constraints upon the domain, image and codomain.