Category:Preorder Theory

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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      \(\displaystyle \forall a, b, c \in S:\) \(\displaystyle a \mathop {\mathcal R} b \land b \mathop {\mathcal R} c \implies a \mathop {\mathcal R} c \)