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3
questions
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Proof of Dedekind cuts.
This is my definition for Dedekind cuts:
A subset α of Q is said to be a cut if:
$α$ is not empty,$α\neq \mathbb{Q}$
If $p \in α,q\in\mathbb{Q}$,and $q<p$,then $q\inα$.
If $p\in α$,then $p<r$ ...
- 97
4
votes
2
answers
172
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Proving the density of a function in an interval.
I am reading Steven G. Krantz's Real Analysis and Foundations and came across this problem.
Problem: Let $\lambda$ be a positive irrational real number. If $n$ is a positive integer, choose by the ...
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3
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4
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Why does a/b have to be in simplest form in the proof of irrationality for sqrt2
The proof of the irrationality of $\sqrt{2}$ starts with the supposition that $\sqrt{2} = \frac ab$ where $a$ and $b$ are integers. I understand that, but why is it important that $\frac ab$ is ...
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