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Homework Help: Analysis proof help please

  1. Dec 15, 2006 #1
    1. Prove if f:R->R is periodic and continuous, then f is uniformly continuous



    2. There exists h that does not equal zero such that f(x+h)=f(x)
     
  2. jcsd
  3. Dec 15, 2006 #2

    matt grime

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    Can you think of any results you know about conditions that make continuous functions into uniformly continuous ones?
     
  4. Dec 15, 2006 #3

    HallsofIvy

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    For 1, I agree with matt grime, Think about theorems that say when a continuous function is uniformly continuous (on a given set of course- "uniform" continuity is always defined on a given set. You want to prove that this function is uniformly continuous on the set of all real numbers. Knowing the function is periodic means you can look at a finite interval!)

    For 2, exactly what is the DEFINITION of "periodic"?
     
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