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Operations with infinity

  1. May 3, 2014 #1
    Is correct to state that:

    ##x \infty = \text{sgn}(x) \infty##

    ##\infty^x = \infty^{\text{sgn}(x)}##

    ?
     
  2. jcsd
  3. May 3, 2014 #2

    HallsofIvy

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    If you are talking about the "usual" real number system, the are NO "operations with infinity" because "infinity" is not a real number. And there are several different ways to create number systems which include "infinity" as a number. Which are you talking about?
     
  4. May 4, 2014 #3
    Your answer complicated more the things... look, exp(-∞) = 0, exp(0) = 1, exp(∞) = ∞... appears make sense make operation with ∞...
     
  5. May 4, 2014 #4

    HallsofIvy

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    Not with the usual real number system, they don't- except a short hand for limits.
    (Not "exp(0)= 1". I have no problem with that and I don't know why you included it here.)
     
  6. May 4, 2014 #5
    For shows that infinity acts like a number...
     
  7. May 4, 2014 #6

    micromass

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    They make sense in some number systems equipped with infinity, but not in others. For example, on the affine real line, the above operations are true, see http://en.wikipedia.org/wiki/Extended_real_number_line
    But on the projective real line, they are false: http://en.wikipedia.org/wiki/Real_projective_line
    There are many other systems which allow an infinity and where the above might make sense or not, so you need to specify.


    I don't see what ##e^0 = 1## has to do with infinity.

    And infinity is certainly not a real number. It might act like on in some ways, but not in others.
     
  8. May 4, 2014 #7
    Hummm, you have more links about this subject?
     
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