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Little integer problem

  1. Aug 28, 2005 #1
    ok,

    a/b c/d

    a,b,c,d are all integers
    b and d are > 0

    find a number inbetween a/b and b/d using a,b,c,d that is an irrational number.

    thanks :!!)
     
  2. jcsd
  3. Aug 28, 2005 #2

    CarlB

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    The difference between the two rational numbers is

    [tex]\frac{ad-bc}{bd}[/tex]

    If you can find an irrational number that is smaller than this, you can add it to the lesser of {a/d, b/c}.

    Carl
     
  4. Aug 28, 2005 #3

    StatusX

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    You could pick a strictly increasing curve (like y=x^2, for x>0), find the x values that generate these two fractions as y values, and find the y value for the number halfway (or anywhere) between these two x values. It's a safe bet this will be an irrational number.
     
  5. Aug 28, 2005 #4
    so that will work for sure carl?
     
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