Has infinity ever cancelled itself out in any Mathematical Equation?

Answer 1

It's common in a calculus class to ask what happens to a quantity like (4x)/(x^2) as x becomes very large.

As x gets big ("approaches infinity"), so do 4x and x^2. We might say that 4x/x^2 approaches "infinity over infinity". We cannot cancel these infinities, however. If we could, that would tell us 4x/x^2 approaches 1, when in fact it approaches 0.

In calculus, people will use the word "infinity", but they aren't talking about a quantity. Many people don't realize that the "infinity" used in calculus is a process, not a number. It's shorthand.

Set theory uses actual infinite quantities, such as Aleph_0 (the number of integers) and 2^(Aleph_0) (the number of real numbers). Arithmetic as we know it does not apply very well to these numbers. For example, half of the integers are even. The number of evens is half the number of integers. However, it can be shown that there are equal numbers of each, so Aleph_0 = (1/2) Aleph_0.

I have not known infinities to cancel each other out, in either context, without some extra information being given. So, to answer your question, I don't think so.

Answer 2

You can cancel out infinity in some types of equations.

x = 1/infinity
You can take x = 0.

Answer 3

Mathematically, there is not one infinity there are many (for instance what is 2 times infinity).

And yes, they cancel all the time in equations. Its a key part of making many equations in physics work. In fact, there is a function defined specifically for some tasks - the Dirac delta function - which is defined to be infinitely high but so narrow that when you integrate over it you get not infinity but precisely 1.