Axiom:Strict Ordering Axioms

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

Formulation 1
$\RR$ satisfies the strict ordering axioms (on $S$) $\RR$ satisfies the  axioms:

Formulation 2
$\RR$ satisfies the strict ordering axioms (on $S$) $\RR$ satisfies the  axioms:

Also see

 * Axiom:Strict Ordering Axioms/Formulation 1 for an alternative formulation of the strict ordering axioms
 * Definition:Strict Ordering
 * Equivalence of Definitions of Strict Ordering