Definition:Preordering/Definition 1

Definition
Let $S$ be a set. A preordering on $S$ is a relation $\mathcal R$ on $S$ such that:

Symbols used to define such a general preordering relation are often variants on $\lesssim$, $\precsim$ or $\precapprox$.

A symbol for a preordering can be reversed, and the sense is likewise inverted:


 * $a \precsim b \iff b \succsim a$

Also see

 * Equivalence of Definitions of Preordering