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Need help analysing a particular set

  1. May 31, 2014 #1
    1. The problem statement, all variables and given/known data

    For the set S = (-1)^n * (3 + 5/n)
    I have determined that the maximum is 3 + 5/2 and the minimum is -8. However I am not sure if it is closed; given that it has a maximum and minimum, does this mean by definition that the set will be closed?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 31, 2014 #2

    hilbert2

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    Science Advisor
    Gold Member

    The number 3 is a limit point of the set, which means that for any ##\epsilon>0## we have a value ##x\in S## such that ##|x-3|<\epsilon##. However, 3 itself is not contained by the set ##S##. Search with google for "closed set limit points" and you will find the answer to your question.
     
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