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Math Help - Are periodic functions uniformly continuous?

  1. #1
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    Are periodic functions uniformly continuous?

    I think it is, here is my proof:

    Suppose that f: \mathbb {R} \mapsto \mathbb {R} is a t-periodic function. We will show that f is uniformly continuous.

    Let  \epsilon > 0 , find  \delta > t such that  x \in \mathbb {R} with  y = x + t , then  |x-y| = | x - x + t | = |-t| = t < \delta

    We then have  |f(x) - f(y) | = |f(x) - f(x + t)| = |f(x)-f(x)| =0 < \epsilon , thus proves the claim.

    Is this right? Thank you.
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    Is this right?
    The statement is wrong how it is stated.
    Consider the sawtooth wave.
    Maybe you also had the condition that f is continous?
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  3. #3
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    It was a problem from a while back, so I do believe I missed the continuity part.
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