Category:Preorder Theory

From ProofWiki
Jump to navigation Jump to search

This category contains results about Preorder Theory.
Definitions specific to this category can be found in Definitions/Preorder Theory.

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

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