Dedekind cut
Regard one Dedekind cut ("A", "B") as "less than" another Dedekind cut ("C", "D") (of the same superset) if "A" is a proper subset of "C". Equivalently, if "D" is a proper subset of "B", the cut ("A", "B") is again "less than" ("C", "D"). In this way, set inclusion can be used to represent the ordering of numbers, and all other relations ("greater than", "less than or equal to", "equal to", and so on) can be similarly created from set relations.