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An algebraic brickwall (real analysis)

  1. Aug 28, 2010 #1
    Goal: to show yn=x

    This particular part of the proof supposes that yn>x. So we want
    an h>0 such that (y-h)n>x

    yn-(y-h)n<yn-x

    yn-(y-h)n=(y-(y-h))(yn-1+yn-2(y-h)+...+(y-h)n-1)<hnyn-1

    this yields h=(yn-x)/(nyn-1)


    my question: how the heck does one derive h from this????
     
  2. jcsd
  3. Aug 29, 2010 #2

    mathman

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    Science Advisor

    You are missing part of the problem statement. What are x and y?
     
  4. Aug 29, 2010 #3
    n is an integer, x and y are reals.

    Sorry bout that.
     
  5. Aug 29, 2010 #4

    epenguin

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    Seems to me you are still missing some of the problem statement. Maybe it needs to be of the form for all or for some something and something there exists something such that yn = x ?

    With the somethings being integer and reals in some combination.
    I think some for arrangements of somethings and the all/some the statement will be false, for others it will be trivial, maybe there is a nontrivial true case?
     
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