\begin{definition}[Definition:Injection/Definition 1]
A mapping $f$ is '''an injection''', or '''injective''' {{iff}}:
:$\forall x_1, x_2 \in \Dom f: \map f {x_1} = \map f {x_2} \implies x_1 = x_2$
That is, an '''injection''' is a mapping such that the output uniquely determines its input.
\end{definition}