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What does lim=infinity mean?

  1. Oct 21, 2007 #1
    I can't believe I'm asking this, because I should know this answer but I'm now doubting myself.

    If a function goes to infinity as x approaches some real number, would we say the limit as x approaches that number is infinity or would we say that it does not exist?

    Doesn't the limit always have to be a real number, but infinity isn't one?

    So for example:
    the limit as x approaches 0 from the right of 1/x is infinity or not defined?
     
  2. jcsd
  3. Oct 21, 2007 #2

    EnumaElish

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    It is a question of whether you are in the reals or the extended reals. The latter includes infinity.
     
  4. Oct 21, 2007 #3
    Generically people will say the limit equals infinity. Indeed infinity is not a real number, but it is useful to use the shorthand of saying the limit equals infinity, as this is more specific than just saying that the limit is undefined.
     
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