 Suppose that formula_25 is a family of preordered vector spaces and that the positive cone of formula_26 is formula_27.Then formula_28 is a pointed convex cone in formula_29, which determines a canonical ordering on formula_29; 
"C" is a proper cone if all formula_27 are proper cones.The algebraic direct sum formula_32 of formula_25 is a vector subspace of formula_29 that is given the canonical subspace ordering inherited from formula_29.