Preorder

Definition

A preordered set is a pair $(S,⩽)$ where $S$ is a set and $⩽$ is a binary relation on $S$ held to the following expectations:

reflexivity

for any $x\in S$, $x⩽x$;

transitivity

for any $x,y,z\in S$, $x⩽y$ and $y⩽z$ together imply $x⩽z$.

Equivalently, a preorder is a partial order sans the antisymmetry law.