\begin{definition}[Definition:One-to-One Relation]
A relation $\RR \subseteq S \times T$ is '''one-to-one''' if it is both many-to-one and one-to-many.
That is, every element of the domain of $\RR$ relates to no more than one element of its codomain, and every element of the image is related to by exactly one element of its domain.
\end{definition}