# -1/0^2 = inf

1. Apr 4, 2006

### cscott

Why does my calculator tell me -1/(0^2) = -infinity. How is this different from 1/0?

2. Apr 4, 2006

### Euclid

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
3. Apr 4, 2006

### dav2008

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
4. Apr 4, 2006

### cscott

Alright, thanks.

...and I agree, Latex is broken.

5. Apr 4, 2006

### TD

Never trust your calculator for mathematical 'subtleties' like this, use your mind

6. Apr 4, 2006

### Hurkyl

Staff Emeritus
Incidnetally, the function

-1/x²

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

-1/x

does not.

7. Apr 4, 2006

### dav2008

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.