Axiom:Preordering Axioms

Definition
Let $\RR \subseteq S \times S$ be a relation on a set $S$.

Formulation 1
$\RR$ satisfies the preordering axioms on $S$ $\RR$ satifies the axioms:

Formulation 2
$\RR$ satisfies the preordering axioms on $S$ $\RR$ satifies the axioms:

Also see

 * Definition:Preordering


 * Equivalence of Definitions of Preordering