Hello. I have a question about Dedekind' cut. Problem #20 of Baby rudin's p23 asks: prove why axiom (A5) on page 5 fails if cuts had maximum elements. (A5): To every x in F( a field) corresponds an element -x in F such that x + (-x) = 0. I guess Archimedean property is a starting point to prove A5 fails. To do that I need to understand the relation between the existence of largest element and Archimedean Property. In what sense are they related? I am puzzled. Please help me out.