Definition:Strict Weak Ordering
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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 $\RR'$ defined as:
- $a \mathrel {\RR'} b := \neg \paren {a \mathrel \RR b} \land \neg \paren {b \mathrel \RR a}$
- is transitive.
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