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what is

infinity+(-infinity)
infinity-infinity
infinity/infinity
0.infinity

2006-09-05 05:45:10 · 24 answers · asked by more1708_par 2 in Science & Mathematics Mathematics

24 answers

To make it clear I'd explain you that there are three different definitions of infinity when we are talking about calculating, for example, limits.
There is a (+infinity), a (-infinity) and an (infinity).
When we manage to calculate
x*y, x/y, x+y, x-y ,
where x and y are one of the infinities described above, the result is undefined.
It means that within the given conditions we cannot determine if
the result is zero, one of the infinities or just a constant.
I'll give an example. Lets assume we want to count
lim(+infinity/-infinity), where x --> +infinity
1) If the fraction is (x^2)/(-x) then the result is +infinity
2) (x^2)/(-x^3) is zero
3) (x^2)/(-x^2) equals -1
I intend the limits, of course.
So to answer your question:
infinity+(-infinity) undefined
infinity-infinity undefined
infinity/infinity undefined
"Undefined" doesn't mean I cannot calculate it, it means, as I said above, that "the result cannot be defined within the given conditions"
I hope I demystified you mind =)
----------------------------------------------
0.infinity
OMG, WTF is that? :P

2006-09-05 06:42:06 · answer #1 · answered by Anonymous · 0 0

None of these are defined. When they arise, almost always in limits, we need to find ways to equate them to something that is defined. In general, they could all be equal to infinity, -infinity, or 0, or some finite number.

infinity + (-infinity) is the sam as infinity - infinity. Suppose this is the limit as x goes to infinity of x - (x + 3). x goes to infinity, and so does x + 3, so you have infinity - infinity. But you can combine terms to simply get -3. So the limit of this expression as x goes to infinity is just -3. On the other hand, the limit as x goes to infinity of x^2 - x is also infinity - infinity, because x^2 and x both go to infinity. In this case, x is negligible as x goes to infinity, because the largest power dominates. This limit is asymptotic with x^2, and goes to positive infinity. So infinity - infinity only has an answer when it arises from a particular expression; it's undefined in the abstract.

For infinity/infinity, when the numerator and the denominator are polynomials, we ignore all but the dominant term in each. If the powers of x are the same, the limit is the ratio of their coefficients, a finite value. If the numerator has a greater order than the denominator, the limit goes to zero. If the denominator has the greater order, the limit goes to infinity or negative infinity, depending on the signs of the coefficients.

0 * infinity is similar. e^-x * x^2 has a limit of zero as x goes to infinity, because e^-x decreases faster than x^2 increases. In fact, e^-x is generally considered the fastest decreasing function; when multiplied by any non-exponential increasing function, the limit is zero. Conversely, an increasing exponential function multiplied by a non-exponential function with decreasing magnitude has a limit of positive or negative infinity, depending on the signs of the factors. Other situations require calculus, or approaches similar to the above. Once again, the formula in the abstract is undefined.

2006-09-05 13:07:58 · answer #2 · answered by DavidK93 7 · 1 0

In the real number system, "infinity" is not considered to be one of the set of real numbers and so none of the operations are defined for infinity

2006-09-05 12:56:29 · answer #3 · answered by J F 1 · 0 0

Consider this...

n/n = 1
n/0 = infinity
0/n = 0

therefore, considering the case when n=0, 0=1=infinity

2006-09-05 12:49:34 · answer #4 · answered by Morgy 4 · 0 0

There can only be one infinity, No matter how many times you add subtract or divide..Your answer will always be infinity!!!!

2006-09-05 12:51:39 · answer #5 · answered by Jessica R 1 · 0 0

infinity

2006-09-05 12:46:30 · answer #6 · answered by twinklee_x3 3 · 0 0

Those numbers are whatever value you want them to be.

Infinity does not have any paticular specific value. It means "more than anything else". And amount LESS than anything else is called "infinitesimal" and it may be written as 1/infinity.

2006-09-05 12:48:47 · answer #7 · answered by poorcocoboiboi 6 · 1 0

infinity, is never ending ? Way too much time on our hands :O)

2006-09-05 12:54:54 · answer #8 · answered by hillman7919 2 · 0 0

One

2006-09-05 12:46:55 · answer #9 · answered by imm 1 · 0 0

that is simple as infinitty is neverending so adding subtracting squarin etc. would do nothing the answer is infinity to all the questions

2006-09-05 12:48:55 · answer #10 · answered by Anthony L 1 · 0 0

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