 If "M" is a vector subspace of "X" then the canonical ordering on "M" induced by "X"'s positive cone "C" is the partial order induced by the pointed convex cone "C" ∩ "M", where this cone is proper if "C" is proper.Let "M" be a vector subspace of an ordered vector space "X", formula_15 be the canonical projection, and let formula_16.Then formula_17 is a cone in "X"/"M" that induces a canonical preordering on the quotient space "X"/"M".