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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.

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# What if one of Dedekind cut's properties were omitted?

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