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Math Help - Sequences

  1. #1
    Newbie
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    Oct 2009
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    Sequences

    Hey all, I'm having a little trouble getting started with this one as I'm really not understanding the hypothesis. Thanks for the help.

    Prove that if (sn) is a sequence of distinct terms in R, s is an element in R and every nonempty open subset containing s contains all but finitely many members of the set (sn: n is an element of natural numbers} then sn converges to s.
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  2. #2
    Senior Member
    Joined
    Feb 2008
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    Choose \epsilon>0. Then (s-\epsilon,s+\epsilon) excludes finitely many s_n. Then there is an integer N=1+\max\{n:s_n\notin(s-\epsilon,s+\epsilon)\} such that if n\geq N then s-\epsilon<s_n<s+\epsilon.

    That's the definition of convergence.
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