Axiom:Ordering Axioms/Formulation 1

Definition
Let $S$ be a set.

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

$\RR$ satisfies the ordering axioms on $S$ $\RR$ satisifes the axioms:

Also see

 * Axiom:Ordering Axioms/Formulation 2 for an alternative formulation of the ordering axioms on a set.
 * Axiom:Ordering Axioms/Class Formulation for a formulation of the ordering axioms on a class.
 * Equivalence of Definitions of Ordering