 If "R" and "S" are two orderings of a vector space with positive cones "P" and "Q", respectively, then we say that "R" is finer than "S" if "P" ⊆ "Q".The real numbers with the usual ordering form a totally ordered vector space.For all integers "n" ≥ 0, the Euclidean space ℝ"n" considered as a vector space over the reals with the lexicographic ordering forms a preordered vector space whose order is Archimedean if and only if "n" = 0 or 1.