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-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


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    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


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    Homework Helper

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


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    Incidnetally, the function


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


    does not.
  8. Apr 4, 2006 #7


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    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.
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