Preorder

Common card · No. 336885

In mathematics, in particular in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. The name preorder is meant to suggest that preorders are almost partial orders, but not quite, as they are not necessarily antisymmetric. A natural example of a preorder is the divides relation "x divides y" between integers. This relation is reflexive as every integer divides itself. It is also transitive. But it is not antisymmetric, because e.g. 1 {\displaystyle 1} divides − 1 {\displaystyle -1} and − 1 {\displaystyle -1} divides 1 {\displaystyle 1} , but − 1 {\displaystyle -1} is not equal to 1 {\displaystyle 1} . It is to this preorder that "least" refers in the phrase "least...

Read on Wikipedia · Image Caleb Stanford, CC0