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Math Help - covergence of a function and sequences

  1. #1
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    covergence of a function and sequences

    Hi can anyone help me with this question please:

    If f:E->R is continous at c and (xn) is a sequence of points in E converging to c, prove that f(xn)->f(c) as n tends to infinity.

    I think that c is an accumlation point and i tried to use its properties but i got nowhere

    Thank you
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  2. #2
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    Here is a very intuitive approach to this problem.
    If f is continuous at c\in E then if x \approx c, x is near c, then f(x)\approx f(c).

    Now to say that \left( {c_n } \right) \to c means that almost all the terms of \left( {c_n } \right) are near c.
    So does it not follow that almost all the terms of \left( f({c_n }) \right) are near f(c)?

    That is the outline of a proof.
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