Definition:Directed Preordering

Definition
Let $D$ be a set.

Let $\leq$ be a preordering on $D$.

Let:
 * $\forall a, b \in D: \exists c \in D: \left({a \le c}\right) \land \left({b \le c}\right)$

Then $\left({D, \le}\right)$ is a directed set.