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Math Help - convergence

  1. #1
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    convergence

    Construct a sequence { x_{n}} of reals such that a = \sup{x_{n}:n\in N} exists, a is not the limit of x_{n} and for every \epsilon\ge 0 and k a positive integer, there exists a positive integer N greater than k such that the absolute value of ( x_{n}-a) is less than \epsilon
    Last edited by Plato; April 20th 2010 at 07:11 AM. Reason: messed up the latex
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  2. #2
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    Quote Originally Posted by janae77 View Post
    Construct a sequence { x_{n}} of reals such that a = \sup{x_{n}:n\in N} exists, a is not the limit of x_{n} and for every \epsilon\ge 0 and k a positive integer, there exists a positive integer N greater than k such that the absolute value of ( x_{N}-a) is less than \epsilon
    Simplest example: x_n=(-1)^n
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