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Real Analysis Continuity

  1. Nov 7, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove that if f is uniformly continuous on [a,b] and on [a,c] implies that f is uniformly continuous on [a,c].

    2. Relevant equations


    3. The attempt at a solution

    This is my rough idea for a proof, can someone help be say this more formally? Is my thinking even correct?

    Let epsilon > 0.
    Then there is some delta_1 for [a,b] and some delta_2 for [b,c].
    Then the minimum of delta_1 and delta_2 is the delta we want for [a,c].
     
  2. jcsd
  3. Nov 7, 2012 #2

    Dick

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    Sure, that's the idea. It's not that hard to fill that out to a formal proof.
     
  4. Nov 7, 2012 #3
    Thanks. What changes should I make to make it more formal?
     
  5. Nov 7, 2012 #4

    Dick

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    Just fill in some words. "there is some delta_1 for [a,b]" doesn't mean much. There is some delta_1 for [a,b] such that what? I know what you mean, but spell it out.
     
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