Real Analysis

[Sheff]

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?

[Country Boy]

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.