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Real Analysis

Sheff
in Homework Help

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Let S = [0,1]. If x and y are in s with x ≠y. How can we show that there are m,n∈N such that x< m/2^n <y. Can the Archimedean Property be used to prove this? If yes, could anyone provide me an insight to do this?

Yes, you should use the Archimedian property here. To start, look at y- x and show that there exist an integer n such that n(y- x) is larger than 1.

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