\begin{definition}[Definition:Serial Relation]
Let $\RR \subseteq S \times S$ be a relation in $S$.
$\RR$ is '''serial''' {{iff}}:
:$\forall x \in S: \exists y \in S: \tuple {x, y} \in \RR$
That is, a relation $\RR \subseteq S \times S$ is '''serial''' {{iff}} every element of $S$ relates to some other element of $S$.
\end{definition}