Definition:Image (Relation Theory)/Mapping/Mapping

Definition
Let $f: S \to T$ be a mapping. The image (or image set) of a mapping $f: S \to T$ is the set:


 * $\operatorname{Im} \left ({f}\right) = \left\{ {t \in T: \exists s \in S: f \left({s}\right) = t}\right\}$

Also denoted as
$\operatorname {Im} \left ({f}\right)$ is frequently rendered as $f \left [{S}\right]$.

Also known as
Some sources refer to this as the direct image of a mapping, in order to differentiate it from an inverse image.

Rather than apply a mapping $f$ directly to a subset $A$, those sources prefer to define the mapping induced by $f$ as a separate concept in its own right.

Also seen is the term image set of mapping for $\operatorname{Im} \left ({f}\right)$.

Also see

 * Definition:Domain of Mapping
 * Definition:Codomain of Mapping
 * Definition:Range


 * Definition:Preimage of Mapping (also known as an inverse image)