Category:Definitions/Preorder Theory

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

$\RR$ is a preordering on $S$ if and only if $\RR$ satifies the preordering axioms:

$(1)$	$:$		$\RR$ is reflexive	$\ds \forall a \in S:$	$\ds a \mathrel \RR a $
$(2)$	$:$		$\RR$ is transitive	$\ds \forall a, b, c \in S:$	$\ds a \mathrel \RR b \land b \mathrel \RR c \implies a \mathrel \RR c $

Subcategories

This category has the following 2 subcategories, out of 2 total.

The following 23 pages are in this category, out of 23 total.

\((1)\)	$:$		$\RR$ is reflexive	\(\ds \forall a \in S:\)	\(\ds a \mathrel \RR a \)
\((2)\)	$:$		$\RR$ is transitive	\(\ds \forall a, b, c \in S:\)	\(\ds a \mathrel \RR b \land b \mathrel \RR c \implies a \mathrel \RR c \)