1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor

    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


    User Avatar
    Science Advisor

    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
    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?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Operations with infinity
  1. Infinity ? (Replies: 3)

  2. Is infinity = infinity? (Replies: 20)