Category:Examples of Orderings

This category contains examples of Ordering/Definition 1.

$\RR$ is an ordering on $S$ if and only if $\RR$ satisfies the ordering 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 $
$(3)$	$:$	$\RR$ is antisymmetric	$\ds \forall a, b \in S:$	$\ds a \mathrel \RR b \land b \mathrel \RR a \implies a = b $

Pages in category "Examples of Orderings"

The following 12 pages are in this category, out of 12 total.

\((1)\)	$:$	$\RR$ is reflexive	\(\ds \forall a \in S:\)	\(\ds a \mathrel \RR a \)
\((2)\)	$:$	$\RR$ is transitive	\(\ds \forall a, b, c \in S:\)	\(\ds a \mathrel \RR b \land b \mathrel \RR c \implies a \mathrel \RR c \)
\((3)\)	$:$	$\RR$ is antisymmetric	\(\ds \forall a, b \in S:\)	\(\ds a \mathrel \RR b \land b \mathrel \RR a \implies a = b \)