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Math Help - Analysis

  1. #1
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    Analysis

    I need to prove that if f and g are continuous functions at z' in C (complex) then so is f - g. Any help would be greatly appreciated. Thanks.
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  2. #2
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    Quote Originally Posted by Louise View Post
    I need to prove that if f and g are continuous functions at z' in C (complex) then so is f - g.
    Just note that \left| {\left[ {f - g} \right](z) - \left[ {f - g} \right](z')} \right| \leqslant \left| {f(z) - f(z')} \right| + \left| {g(z) - g(z')} \right|.
    Each of the last two can be made  < \frac{\epsilon }{2}.
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