Re: Rudin and Dedekind cuts

But surely there is a fundamental difference. To define rationals we can start with the Peano axioms for integers and then define rationals as ordered pairs of integers. The idea of a 'number' is very clear, there is no ambiguity.

With Dedekind cuts, there IS ambiguity.

I appreciate that I can define reals using Cauchy sequences, but I am trying to understand the Dedekind cuts.
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Relevant Pages

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