then the property known as "transitivity of incomparability" (defined below) is exactly the condition necessary and sufficient to guarantee that the relation "are -equivalent" does indeed form an equivalence relation on When this is the case, it allows any two elements satisfying to be identified as a single object (specifically, they are identified together in their common equivalence class).

Definition

A strict weak ordering on a set is a strict partial order

1.Previous
3.Next