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Math Help - Sequence of functions

  1. #1
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    Sequence of functions

    Let (fn) be a sequence of functions from R to R, not necessarily continuous. Suppose that for all sequences (xn) such that (xn)-->x as n--> inf, we have:

    (fn(xn)) --> f(x) as n-->inf and (xn)-->x

    Prove that f is continuous.

    PS: No specific metric is identified
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by southprkfan1 View Post
    Let (fn) be a sequence of functions from R to R, not necessarily continuous. Suppose that for all sequences (xn) such that (xn)-->x as n--> inf, we have:

    (fn(xn)) --> f(x) as n-->inf and (xn)-->x

    Prove that f is continuous.

    PS: No specific metric is identified
    Haven't I already proven this for you in a previous thread?
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  3. #3
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    Quote Originally Posted by Drexel28 View Post
    Haven't I already proven this for you in a previous thread?
    No. That was a different question.
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