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Homework Help: I need help solving a proof dealing with the set of irrational numbers.

  1. Oct 4, 2012 #1
    1. The problem statement, all variables and given/known data

    Let x,y,t be in the set of all real numbers (R) such that x<y and t>0. Prove that there exists a K in the set of irrational numbers (R\Q) such that x<(K/t)<y

    2. Relevant equations

    if x,y are in R and x<y then there exists an r in Q such that x<=r<y

    3. The attempt at a solution
    0<x<y implies that 0<(1/y)<(1/x)
     
  2. jcsd
  3. Oct 4, 2012 #2

    jbunniii

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    Hint: if you choose some specific irrational such as [itex]\sqrt{2}[/itex], then the sum of this number plus any rational is irrational.
     
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