# Category:Definitions/Preorder Theory

This category contains definitions related to Preorder Theory.
Related results can be found in Category:Preorder Theory.

$\mathcal R$ is a preordering on $S$ if and only if:

 $(1)$ $:$ $\mathcal R$ is reflexive $\displaystyle \forall a \in S:$ $\displaystyle a \mathrel {\mathcal R} a$ $(2)$ $:$ $\mathcal R$ is transitive $\displaystyle \forall a, b, c \in S:$ $\displaystyle a \mathrel {\mathcal R} b \land b \mathrel {\mathcal R} c \implies a \mathrel {\mathcal R} c$

## Pages in category "Definitions/Preorder Theory"

The following 26 pages are in this category, out of 26 total.