 A subset "A" of a vector lattice "E" is called order complete if for every non-empty subset "B" ⊆ "A" such that "B" is order bounded in "A", both formula_4 and formula_5 exist and are elements of "A".We say that a vector lattice "E" is order complete is "E" is an order complete subset of "E".Finite dimensional vector lattices fall into one of two categories depending on whether or not the lattice is Archimedean ordered.