# How useful is infinity? [closed]

If infinity in one case is just something that cannot be capped. Does it really find its use in something? Speed is a number and when Dr.Math can assume it can be infinite, in reality universe even slows down time to make it a capped by a finite number.

I am sure there should be some transformation that makes an infinity transform into a number suddenly depending on what it defines? Could there be just infinite constants that we just dont know instead of infinity itself?

Is there something where infinity helps than being a number?

Ok My question is. I consider infinity is a limitation. Its an assumption that something is limitless. So at some point infinity becomes a number when we know that limit. So my question is does infinity helped with any mathematical achievements. In other words even if we know speed limited by speed of light mathematically speed can be infinity but not physically. Has it helped in anyway to assume speed can be infinity and proved something or disproved something.

-

## closed as unclear what you're asking by Avitus, Norbert, mrf, TZakrevskiy, egregDec 5 '13 at 11:49

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question.If this question can be reworded to fit the rules in the help center, please edit the question.

This guy should transfer from math to philosophy. –  Adam Dec 5 '13 at 12:03
@Adam I was never in Math to transfer! –  Dexters Dec 6 '13 at 3:46
I'm not sure what you mean by "at some point infinity becomes a number". I'm also not sure why you consider infinity a limitation of mathematics. When mathematicians work with infinity they are working with precise and unambiguous definitions. Most misconceptions regarding infinity only arise because people refuse to accept a working definition of "infinity". –  EuYu Dec 6 '13 at 4:01
@Adam: To the best of my knowledge, the philosophers concluded that mathematics has the right approach to the subject. –  Hurkyl Dec 6 '13 at 4:08
@Dexters People really didn't know much about the universe as a whole until perhaps the early to mid 20th century. The assumption that the universe is infinite seemed like the most reasonable one at the time (and still is), but it was not made without scrutiny. Olber's paradox is one famous problem regarding the assumption that the universe is infinite. My point is that assumptions in science have consequences. If the consequences of your assumption is incompatible with reality then simply put, your assumption is wrong. All that being said, I still don't understand what your question is. –  EuYu Dec 6 '13 at 4:27

Geometrically, $\Bbb R^n\cup\{\infty\}$ is homeomorphic to $S^n$, or the $n$-dimensional hypersphere. This also allows for geometry on the upper-half plane and Mobius inversions (generally, projective geometries make good use of infinity).
Infinity is also used for limits and series (e.g. $e=\lim_{n\to\infty} \left(1+\frac1n\right)^n=\sum_{n=0}^\infty \frac1{n!}$). These series play a fundamental role in one of the nice proofs of the identity $e^{ix}=\cos x+i\sin x$.
Well, no, for all finite $\alpha$, $\sum_{n=0}^\alpha \frac{1}{n!}$ is rational, while $e$ is transcendental, so clearly $\infty$ can't be defined as "an arbitrarily large finite number." –  Tim Ratigan Dec 5 '13 at 11:37