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Math Help - Real Analysis - Uniform Conv

  1. #1
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    Real Analysis - Uniform Conv

    If fn --> f uniformly on a set A, and if fn --> f uniformly on a set B, then fn --> f uniformly on A U B.

    This is the last question I need to answer. I can't really figure it out because there's nothing similar to this question in the book's examples.
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  2. #2
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    Idea

    I think the answer is false, but I can't think of a viable counterexample.
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  3. #3
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    Quote Originally Posted by ajj86 View Post
    If fn --> f uniformly on a set A, and if fn --> f uniformly on a set B, then fn --> f uniformly on A U B.
    You have an integer N_A to use with set A.
    You have an integer N_B to use with set B.
    If N=N_A + N_B would that work on A \cup B?
    Why or why not?
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