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Math Help - Non-convergent sequences in metric spaces

  1. #1
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    Non-convergent sequences in metric spaces

    I need to prove that in any metric space containing more than one point exists a non-convergent sequence. This seems easy enough, but after wrestling with definitions of the metric space and the limit of a sequence I can't seem to produce a proof. Do I need to know more to prove this?
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  2. #2
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    Quote Originally Posted by iligabor View Post
    I need to prove that in any metric space containing more than one point exists a non-convergent sequence. This seems easy enough, but after wrestling with definitions of the metric space and the limit of a sequence I can't seem to produce a proof. Do I need to know more to prove this?

    Let x,y, be two different points in a metric space. What about the seq. x_n=\left\{\begin{array}{ll}x&if\,\,n\,\,is\,\,odd  \\y&if\,\,n\,\,is\,\,even\end{array}\right. ?

    Tonio
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  3. #3
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    Thank you, now I see it.
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