Axiom:Strict Ordering Axioms/Formulation 1

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

$\RR$ is a strict ordering on $S$ $\RR$ satisfies the  axioms:

These criteria are called the strict ordering axioms.

Also see

 * Axiom:Strict Ordering Axioms/Formulation 2 for an alternative formulation of the strict ordering axioms
 * Definition:Strict Ordering
 * Equivalence of Definitions of Strict Ordering