\begin{definition}[Definition:Image of Subset under Mapping/Definition 1]
Let $S$ and $T$ be sets.
Let $f: S \to T$ be a mapping.
Let $X \subseteq S$ be a subset of $S$.
The '''image of $X$ (under $f$)''' is defined and denoted as:
:$f \sqbrk X := \set {t \in T: \exists s \in X: \map f s = t}$
\end{definition}