\begin{definition}[Definition:Relation/Relation as Ordered Pair]
Some sources define a relation between $S$ and $T$ as an ordered pair:
:$\struct {S \times T, \map P {s, t} }$
where:
:$S \times T$ is the Cartesian product of $S$ and $T$
:$\map P {s, t}$ is a propositional function on ordered pairs $\tuple {s, t}$ of $S \times T$.
Note that this approach leaves the domain and codomain inadequately defined.
This situation arises in the case that $S$ or $T$ are empty, whence it follows that $S \times T$ is empty, but $T$ or $S$ are not themselves uniquely determined.
\end{definition}