Definition:Preordering/Definition 2

Definition
Let $\RR \subseteq S \times S$ be a relation on a set $S$. $\RR$ is a preordering on $S$ :
 * $(1): \quad \RR \circ \RR = \RR$
 * $(2): \quad \Delta_S \subseteq \RR$

where:
 * $\circ$ denotes relation composition
 * $\Delta_S$ denotes the diagonal relation on $S$.

Also see

 * Equivalence of Definitions of Preordering


 * Definition:Ordering/Definition 2