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Math Help - Continuity Question

  1. #1
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    Continuity Question

    In a few proofs that I have read in Complex Analysis, it uses a property that says:

    If a function f is continuous, then it can be express as f(z)=g(z)+h(z)

    Where h(z) shrinks to zero. Now I'm not sure if the statement is 100% correct, but why is it true?

    Thank you.
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  2. #2
    Super Member Gamma's Avatar
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    What are the conditions on g(z)? otherwise you could just make h(z)\equiv 0 and g(z)\equiv f(z) and the continuity of f(z) is irrelevant.
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