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Ordered Field Question

  1. Feb 24, 2014 #1
    1. The problem statement, all variables and given/known data

    Prove that 139/159 is not an upper bound for the set of real numbers:

    E ={(14n + 11)/(16n + 19): n ε N}
    

    2. Relevant equations



    3. The attempt at a solution

    Right so I let 14n + 11 = 139 and I got n=9.14. Since n is supposed to be natural and the answer I got for n isn't, can I deduce that 139/159 is not an upper bound for E?
     
  2. jcsd
  3. Feb 24, 2014 #2
    You have to find a positive integer such that if you plug it into (14n + 11)/(16n + 19) you get a number greater than 139/159.
    
     
  4. Feb 24, 2014 #3
    Hey shortydeb thanks for the quick reply.

    That is what I originally thought but do I not need to get a number n that lies before and after 139/159 but not exactly on it? Its very tedious work if that is the case :/
     
  5. Feb 24, 2014 #4
    Set (14n + 11)/(16n + 19) equal to 139/159 and see what you get for n.
     
  6. Feb 24, 2014 #5

    Ray Vickson

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    No. All you need do is find an integer n giving the fraction > 139/159. You do not need to find the "best" or "nearest" n, or anything like that.
     
  7. Feb 24, 2014 #6
    Ok I get it now so. Thanks for the help much appreciated
     
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