Definition:Strict Weak Ordering

Definition
A strict weak ordering on a set $S$ is a relation $\RR$ such that:


 * $(1): \quad \RR$ is a strict partial ordering


 * $(2): \quad$ The incomparability relation $\mathcal R'$ defined as:


 * $a \mathrel {\RR'} b := \neg \paren {a \mathrel \RR b} \land \neg \paren {b \mathrel \RR a}$


 * is transitive.