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Math Help - Need clarification on this problem

  1. #1
    Junior Member
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    Need clarification on this problem

    So I'm doing a little self-study in Kirkwood's Introduction to Analysis, and I need some clarification on something. Exercise 8 (a) in chapter 5-1 is this:

    Suppose |f(x+h)-f(x)| \le Kh^{\alpha} for some constant K and \alpha > 0. Show that f is continuous.

    This doesn't make any sense if h < 0, since \alpha = {1\over 2} makes Kh^{\alpha} complex. However, the problem never states h \ge 0. I don't think that's implied either, since it looks like the result can be proven if we revise it to say |f(x+h)-f(x)| \le K|h|^{\alpha}.

    I don't need, nor do I want help with the proof, only in clarifying this apparent typo. Thoughts?
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  2. #2
    Senior Member Tinyboss's Avatar
    Joined
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    Re: Need clarification on this problem

    Yes, I think your modification is what the question is trying to ask.
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