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Having a hard time understanding this

  1. Nov 11, 2012 #1

    Zondrina

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    Homework Helper

    This question was posted in the homework forum. To my understanding, this looks like two different questions as the first hypothesis is not true due to a simple counter-example argument. The second one would be true by two induction arguments on k>2 and k<0.

    Am I wrong in thinking this? It seems logical since he said "there exists a c >1" so I would figure any REAL c must make the inequality true?
     
    Last edited: Nov 11, 2012
  2. jcsd
  3. Nov 11, 2012 #2
    I would use induction on this. The wording is pretty awkward and it seems like two different questions but I think they are looking for an induction type proof.
     
  4. Nov 11, 2012 #3

    LeonhardEuler

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    Zondrina, I had the same confusion as you when I first read the question. It is actually only one question. The first part is not saying
    " if m>1 then there exists a c>1 that satisfies
    cm<mc"
    The whole thing is saying that if the number "m" is such that some "c" exists satisfying the requirement, then every k>c satisfies the second inequality.
     
  5. Nov 11, 2012 #4

    Zondrina

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    Yes this makes sense now, thank you. If that were the case though, would I have been wrong to say that?

    I thought he meant for every m>1, there exists a c>1 which satisfies .. blah.
     
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