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Constant functions

  1. Jan 15, 2010 #1
    1. The problem statement, all variables and given/known data
    Hi all

    How can I show that a constant function defined on a closed interval is continuous on that same interval using a ε-δ proof?

    I have f(x)=c on the interval. Then I write

    f(x)-f(a) = c-c = 0

    for some point a in the interval. But what to do from here?
  2. jcsd
  3. Jan 15, 2010 #2


    Staff: Mentor

    This is a very easy proof. Isn't 0 < epsilon for any positive epsilon?
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