A weak order satisfies: completeness /\ transitivity. A weak order is commonly denoted as "=>". (=> also satisfies reflexivity) From a weak order you can build a strong order and equivalence as follows: x~y <=> x=>y /\ y=>x x>y <=> x=>y /\ y!=>x There is a theorem which states that the above definitions lead to each other. X/~ == {{x}: x in X, forall y in {x} y~x} is a partition of the set into equivalence classes.