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Number systems: construction of rational numbers

  1. Apr 28, 2012 #1
    1. The problem statement, all variables and given/known data

    let a and b be rational numbers
    if a>b>0
    show that there exists a natural number n, which can be considered rational as well, st
    nb>a

    2. Relevant equations



    3. The attempt at a solution

    I was trying using the peano theorem of natural numbers

    define set of natural numbers st n E S.
    Assume n =1
    (1)b = b
    we know that b <a. hence 1 E N.

    Assume n E n. then n' E n
    n'b >a
    (n+1)b
    bn +b
    b(1) + b
    2b

    I am kinda confused need some help in this thanks very much
     
  2. jcsd
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