Category:Definitions/Preorder Theory

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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      \(\ds \forall a, b, c \in S:\) \(\ds a \mathrel \RR b \land b \mathrel \RR c \implies a \mathrel \RR c \)