\begin{definition}[Definition:Injection/Definition 4]
Let $f$ be a mapping.
$f$ is an '''injection''' {{iff}}:
:$\forall y \in \Img f: \card {\map {f^{-1} } y} = \card {\set {f^{-1} \sqbrk {\set y} } } = 1$
where:
:$\Img f$ denotes the image set of $f$
:$\card {\, \cdot \,}$ denotes the cardinality of a set
:$\map {f^{-1} } y$ is the preimage of $y$
:$f^{-1} \sqbrk {\set y}$ is the preimage of the subset $\set y \subseteq \Img f$.
That is, {{iff}} the preimage of $y$ is a singleton for all $y$ in the image set of $f$.
\end{definition}