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Limit problem, theory very basic question

  1. Aug 15, 2011 #1
    1. The problem statement, all variables and given/known data


    I remember I got it wrong way back in calculus I over this concept.

    If I have

    lim f(x) = ∞
    x→∞

    Would it be right to say the limit does not exist? I remember my professor said it was wrong because it does exist and it is infinity.
     
  2. jcsd
  3. Aug 15, 2011 #2
    It doesn't exist on ℝ. However, it does exist on ℝ∪{−∞, +∞}. The latter is usually written as ℝ with a bar over it, but I don't know how to type that.
     
    Last edited: Aug 15, 2011
  4. Aug 15, 2011 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Harrisonized is talking about the "extended real number system". But, in Calculus, you seldom mention that. Typically, in calculus, it is best to think of "[itex]lim f(x)= \infty[/itex] as just meaning "f(x) does not have a limit (for a particular reason)".
     
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