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Analysis problem

  1. Nov 12, 2008 #1
    Let x_{0} element of N. Then there is a sequence (x_{n}) that converges at x_{0} but has no terms that are nutural numbers.

    Is that true?

    Thank you
     
  2. jcsd
  3. Nov 12, 2008 #2
    Welcome tp PF.

    What do you mean by a sequence to converge at some point?

    If you ask if a sequence of real numbers all of whose term are not natural numbers can converge to some natural number, the answer is yes. I assume, you prefer trying to prove it yourself to being given a hint right away.
     
  4. Nov 12, 2008 #3

    HallsofIvy

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    Can you think of a sequence that converges to 0? Does that meet the requirements?
     
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