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Math Help - uniform continuity theorem

  1. #1
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    uniform continuity theorem

    The uniform continuity theorem says if f: A->N is continuous and Kin A is compact, then f is uniformly continuous on K.

    But if I take 1/n on [0,1] it is not uniformly continuous because as we approach 0 from the left the y values get further and further apart. Is tehre something I'm missing in this theorem?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by cp05 View Post
    The uniform continuity theorem says if f: A->N is continuous and Kin A is compact, then f is uniformly continuous on K.

    But if I take 1/n on [0,1] it is not uniformly continuous because as we approach 0 from the left the y values get further and further apart. Is tehre something I'm missing in this theorem?
    This makes no sense whatsoever. What's your function? Are you saying that f\left(\frac{1}{n}\right) isn't Cauchy?
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  3. #3
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    I meant f=1/x, f:[0,1] -> R
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  4. #4
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    f is not defined at 0, therefore not continuous there. That theorem requires (although you didn't state it) that f is continuous in K.
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