\begin{definition}[Definition:Bijection/Definition 1]
A mapping $f: S \to T$ is a '''bijection''' {{iff}} both:
:$(1): \quad f$ is an injection
and:
:$(2): \quad f$ is a surjection.
That is, {{iff}} $f$ is a relation which is:
:$(1): \quad$ left-total
:$(2): \quad$ right-total
:$(3): \quad$ functional (many-to-one)
:$(4): \quad$ injective (one-to-many).
\end{definition}