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Homework Help: Subsequences of Xn

  1. Mar 9, 2010 #1
    1. The problem statement, all variables and given/known data
    What are all of the subsequences of {xn}?


    2. Relevant equations
    {xn}={1, 1+1/2, 2, 1-1/2, 1, 1+1/3, 3, 1-1/3, 1, 1+1/4, 4, 1-1/4, 1, ...}


    3. The attempt at a solution
    So far I have:
    {1}, {1+1/n}, {1-1/n} and {n} but I can't find any more... I am pretty sure there are though
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 9, 2010 #2

    Hurkyl

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    Staff Emeritus
    Science Advisor
    Gold Member

    Well, there is

    {1+1/2, 2, 1-1/2, 1, 1+1/3, 3, 1-1/3, 1, 1+1/4, 4, 1-1/4, 1, ...}

    and

    {1, 2, 1-1/2, 1, 1+1/3, 3, 1-1/3, 1, 1+1/4, 4, 1-1/4, 1, ...}



    I doubt there's a reasonable way to describe "the set of all subsequences of xn" in any way other than that description.
     
  4. Mar 9, 2010 #3
    sorry, I miswrote the question, it was "what are the subsequences of {xn}", I think it refers to subsequences that you can define like I did previously using n
     
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