- #1
cscott
- 778
- 1
Why does my calculator tell me -1/(0^2) = -infinity. How is this different from 1/0?
Why is -1/(0²) considered -Infinity while 1/0 is undefined?
- Context: Undergrad
- Thread starter cscott
- Start date
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- Difference Infinity
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Discussion Overview
The discussion centers around the mathematical treatment of expressions involving division by zero, specifically contrasting -1/(0²) and 1/0. Participants explore the implications of these expressions in terms of limits and calculator outputs.
Discussion Character
- Exploratory, Technical explanation, Debate/contested
Main Points Raised
- One participant notes that 1/0 is considered undefined because it approaches infinity from the right and negative infinity from the left, while -1/(x²) approaches negative infinity as x approaches 0 from either direction.
- Another participant suggests that the calculator's behavior regarding 1/0 and -1/(0²) may be due to how it processes these expressions, indicating that calculators may categorize them differently based on the power of zero.
- It is mentioned that for even powers, calculators may return infinity, while for odd powers, they return undefined.
- A participant points out that the function -1/x² has a continuous extension at x=0 in the extended real numbers, unlike -1/x, which does not.
- There is a suggestion that calculators may be computing limits of these functions as they approach zero, leading to different outputs for even and odd functions.
Areas of Agreement / Disagreement
Participants express differing views on the definitions and implications of division by zero, with no consensus reached on the nature of these expressions or the reliability of calculators in handling them.
Contextual Notes
Participants note limitations in calculator outputs and the subtleties of mathematical definitions regarding division by zero, but do not resolve these complexities.
Who May Find This Useful
This discussion may be of interest to those exploring mathematical concepts related to limits, division by zero, and the behavior of functions near singularities.
- #2
Euclid
- 213
- 0
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.
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:
- #3
dav2008
Gold Member
- 589
- 1
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...
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:
- #4
cscott
- 778
- 1
Alright, thanks.
...and I agree, Latex is broken.
...and I agree, Latex is broken.
- #5
TD
Homework Helper
- 1,016
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Never trust your calculator for mathematical 'subtleties' like this, use your mind 
- #6
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
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Incidnetally, the function
-1/x²
does have a continuous extension to x=0 in the extended real numbers. Whereas
-1/x
does not.
-1/x²
does have a continuous extension to x=0 in the extended real numbers. Whereas
-1/x
does not.
- #7
dav2008
Gold Member
- 589
- 1
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.Hurkyl said:
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