# Math Help - Need clarification on this problem

1. ## 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?

2. ## Re: Need clarification on this problem

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