\begin{definition}[Definition:Image (Set Theory)/Mapping/Element]
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 $f$.
\end{definition}