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Math Help - rational numbers

  1. #1
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    rational numbers

    Let r be a rational number greater than 1 and let f:R --> R be a function that satisfies abs(f(y)-f(x)) is less than or equal to (y-x)^r for all x, y in R. Prove that f is continuous on R.
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  2. #2
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    Quote Originally Posted by friday616 View Post
    Let r be a rational number greater than 1 and let f:R --> R be a function that satisfies abs(f(y)-f(x)) is less than or equal to (y-x)^r for all x, y in R. Prove that f is continuous on R.

    Apply the very definition of continuity taking, for any \epsilon>0\,,\,\,\delta=\sqrt [r]{\epsilon}

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