 It is easy to see that no ordered field can be lattice-complete, because it can have no largest element (given any element "z", is larger), so this is not the sense that is meant.Additionally, an order can be Dedekind-complete, as defined in the section Axioms.The uniqueness result at the end of that section justifies using the word "the" in the phrase "complete ordered field" when this is the sense of "complete" that is meant.