\begin{definition}[Definition:Image (Set Theory)/Relation/Element]
Let $\RR \subseteq S \times T$ be a relation.
Let $s \in S$.
The '''image of $s$ by''' (or '''under''') '''$\RR$''' is defined as:
:$\map \RR s := \set {t \in T: \tuple {s, t} \in \RR}$
That is, $\map \RR s$ is the set of all elements of the codomain of $\RR$ related to $s$ by $\RR$.
Thus:
:$\map \RR s$
is another way to write:
:$\RR \sqbrk {\set s}$
where $\RR \sqbrk {\set s}$ denotes the image of a subset of $\RR$.
\end{definition}