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Definition of limit reversed

  1. Feb 3, 2010 #1
    so i have a question. If you reverse the definition of limit, does the error change the meaning?

    original: for each epsilon>0, there exists a delta>0, such that if 0<|x-c|<delta, then |f(x)-L|<epsilon.

    with an error: for each delta>0, there exists an epsilon>0, such that if 0<|x-c|<delta, then |f(x)-L|<epsilon.

    So does this error change the meaning of the definition? thanks
     
  2. jcsd
  3. Feb 4, 2010 #2

    radou

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    Yes, it does. Do you see how?
     
  4. Feb 4, 2010 #3
    no, please explain
     
  5. Feb 4, 2010 #4
    Consider the function f(x) = 1 for all x, c=0, L=2 (and not L=1 as you would expect). Show that this satisfies the new definition, but not the original one.
     
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