# 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 | \(\displaystyle \forall a \in S:\) | \(\displaystyle a \mathop {\mathcal R} a \) | ||||

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

## Pages in category "Preorder Theory"

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