\begin{definition}[Definition:Bijection/Also known as]
The terms
:'''biunique correspondence'''
:'''bijective correspondence'''
are sometimes seen for '''bijection'''.
Authors who prefer to limit the jargon of mathematics tend to use the term '''one-one and onto mapping''' for '''bijection'''.
If a '''bijection''' exists between two sets $S$ and $T$, then $S$ and $T$ are said to be '''in one-to-one correspondence'''.
Occasionally you will see the term '''set isomorphism''', but the term '''isomorphism''' is usually reserved for mathematical structures of greater complexity than a set.
Some authors, developing the concept of '''inverse mapping''' independently from that of the '''bijection''', call such a mapping '''invertible'''.
The symbol $f: S \leftrightarrow T$ is sometimes seen to denote that $f$ is a '''bijection''' from $S$ to $T$.
Also seen sometimes is the notation $f: S \cong T$ or $S \stackrel f \cong T$ but this is cumbersome and the symbol has already got several uses.
== Technical Note ==
{{:Definition:Bijection/Technical Note}}
\end{definition}