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Showing Density in R

  1. Oct 5, 2011 #1
    if u>0 is any real number and x<y show there exist a rational number r such that x<ru<y. Hence {ru: r[itex]\in[/itex]Q is dense in R.

    I am not sure how to show that there exist a rational number. I was thinking this has something to do with the archimedian property. This is what I have tried


    x<[itex]\frac{(x+y)}{2}[/itex]<y

    Define r= [itex]\frac{(x+y)}{2}[/itex](1/n) when u>=1 and
    r=[itex]\frac{(x+y)}{2}[/itex](n) when u<1

    where n is an element of the naturals

    but I dont think that works? Any suggestions?
     
  2. jcsd
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