# Category:Preorder Theory

This category contains results about Preorder Theory.
Definitions specific to this category can be found in Definitions/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 $\displaystyle \forall a, b, c \in S:$ $\displaystyle a \mathrel {\mathcal R} b \land b \mathrel {\mathcal R} c \implies a \mathrel {\mathcal R} c$

## Subcategories

This category has only the following subcategory.

## Pages in category "Preorder Theory"

The following 25 pages are in this category, out of 25 total.