Definition:Image (Relation Theory)/Mapping/Element

Definition
Let $f: S \to T$ be a mapping. Let $s \in S$.

The image of $s$ (under $f$) is defined as:


 * $\Img s = \map f s = \ds \bigcup \set {t \in T: \tuple {s, t} \in f}$

That is, $\map f s$ is the element of the codomain of $f$ related to $s$ by $f$.

By the nature of a mapping, $\map f s$ is guaranteed to exist and to be unique for any given $s$ in the domain of $f$.

Also denoted as
The notation $\Img f$ is specific to.

Also see

 * Definition:Image of Element under Relation