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Construction of Real Number by Dedekind Cuts [closed]
I was studying Axiomatic Set Theory, and I have 2 questions about the construction of real numbers using Dedekind cut:
We define a real number using the Dedekind cut: $x_{\mathbb{R}} = \left \{ p \...
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a problem in Stein's book 'Real analysis', relate to continuum hypothesis.
The question is from chapter 2, problem 5 in Stein's book 'Real analysis':
There is an ordering $≺$ of $\mathbb R$ with the property that for each $y\in\mathbb R$ the set $\{x\in\mathbb R : x ≺ ...
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