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Math Help - Question about limit points in C

  1. #1
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    Question about limit points in C

    Let S be an infinite subset of \overline{\mathbb{C}} (the extended complex plane). Show that either S has a limit point in S or every Disc D'( \infty,r) (punctured disc) contains a point of S (so that \infty is a limit point of S in the space \mathbb{C}).

    My argument so far is:
    Assume S does not have a limit point in S. Then take an abitrary disc D'( \infty,r).
    Now assume for contradiction D'( \infty,r) does not contain a point of S. But I can't see where I can find a contradiction to the first statement. Can someone help, or provide an alternative argument? Thanks
    Last edited by Speed1991; December 18th 2011 at 08:18 AM.
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  2. #2
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    Re: Question about limit points in C

    You have a typo in your post. "SHow that either S has a limit point in S of every Disc", the "of" should be "or".
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  3. #3
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    Re: Question about limit points in C

    if you don't mind please define the punctured disk D'(infinite,r).......what do wanted to mean ...please discuss explicitly......
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