 Then formula_79 is a pointed convex cone in formula_80, which determines a canonical ordering on formula_80; 
"C" is a proper cone if all formula_78 are proper cones.The algebraic direct sum formula_83 of formula_76 is a vector subspace of formula_80 that is given the canonical subspace ordering inherited from formula_80.If "X"1, ..., "X""n" are ordered vector subspaces of an ordered vector space "X" then "X" is the ordered direct sum of these subspaces if the canonical algebraic isomorphism of "X" onto formula_87 (with the canonical product order) is an order isomorphism.