Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

-1/0^2 = inf

  1. Apr 4, 2006 #1
    Why does my calculator tell me -1/(0^2) = -infinity. How is this different from 1/0?
     
  2. jcsd
  3. Apr 4, 2006 #2
    1/0 isn't anything, since 1/x approaches infinity if x --> 0 from the right (x>0) and 1/x approaches -infinity if x --> 0 from the left (x<0).
    By contrast, -1/x^2 is always negative, so it approaches negative infinity as x --> 0 no matter which direction you come from.
    Bear in mind, I'm not saying that -1/0^2 equals - infinity. It's not really defined actually.
    What kind of calculator are you using anyway? Mine always says "error - divide by 0" if I put in 1/0.
     
    Last edited: Apr 4, 2006
  4. Apr 4, 2006 #3

    dav2008

    User Avatar
    Gold Member

    I think his question is why his calculator (TI-89) says 1/0 is undefined but 1/02 says infinity.

    It just has to do with how the calculator calculates things I guess.

    Edit: I tried it for other powers and it seems like a/0n is given as infinity for even n and "undef" for odd n if n is positive.

    If n is negative it gives a/0n as 0. If n is zero it gives it as a, but writes a warning message saying that 00 was replaced by 1.


    Edit: I think latex is broken...
     
    Last edited: Apr 4, 2006
  5. Apr 4, 2006 #4
    Alright, thanks.

    ...and I agree, Latex is broken.
     
  6. Apr 4, 2006 #5

    TD

    User Avatar
    Homework Helper

    Never trust your calculator for mathematical 'subtleties' like this, use your mind :smile:
     
  7. Apr 4, 2006 #6

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Incidnetally, the function

    -1/x²

    does have a continuous extension to x=0 in the extended real numbers. Whereas

    -1/x

    does not.
     
  8. Apr 4, 2006 #7

    dav2008

    User Avatar
    Gold Member

    That makes sense. The calculator is probably computing the limit of those functions as they go to 0, which is infinity for even functions and undefined for odd.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?