# Definition:Serial Relation

## Definition

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 $S$.

## Also see

• Results about serial relations can be found here.