Is infinity minus infinity equal to a finite number?

[Zula110100100]

Title says it all.. is: x+(∞)+(-∞) = x? true?

In the case of an integral broken up over three additions and one yields a number, one yields infinity, the other negative infinity, do the infinities cancel?

 

[Zula110100100]

The FAQ does say that it is undefined, but in the integral I am working on it should be possible to come up with an answer in the situation that causes it to arise.

 

[EnergyHobo]

You shouldn't ever try to add and subtract infinity (it's undefined really). This is one of those indeterminate forms that shouldn't be used. You should be taking the limit of the difference between the two integrals as you approach your bounds.

If you could tell us what you were integrating, that would help tremendously. Once the function is known, more specific help can be given to you.

 

[Zula110100100]

I guess it's that I don't really understand how to use 0+ in the case of like, 1/sin(x), how does that area not add up to infinity? over the range of 0 - pi for instance

 

[chiro]

I guess it's that I don't really understand how to use 0+ in the case of like, 1/sin(x), how does that area not add up to infinity? over the range of 0 - pi for instance

Hey Zula110100100 and welcome to the forums.

Have you (or are you) doing improper integrals?

 

[Jamma]

Clearly not. Take 3 functions, one a small bump function at the origin (with area, say, A), one which is |x|+1 and one which is -|x|.

The areas under the graphs of these 3 are A, ∞ and -∞, respectively. Add the functions together and then take the integral- the function will look like f(x)=1 almost everywhere and will have ∞ as the integral, not A.