Definition:Serial Relation

Let $$\mathcal{R} \subseteq S \times S$$ be a relation in $S$.

$$\mathcal{R}$$ is serial iff:


 * $$\forall x \in S: \exists y \in S: \left({x, y}\right) \in \mathcal{R}$$

That is, a relation $$\mathcal{R} \subseteq S \times S$$ is serial iff every element of $$S$$ relates to some other element of $$S$$.