View Full Version : Infinity - Concept or Number?

February 7th, 2009, 08:17 PM
Do you believe that "infinity" can actually be reached or whether it is just the belief of something that has no bounds?

No, not inspired by TCTI. Just would make for a good debate.

February 7th, 2009, 08:19 PM
I think that it is something that has no bounds. Kinda like love :3

February 7th, 2009, 08:24 PM
Basically as soon as you count to 1 you've counted to infinity since infinity keeps on going. :3

February 7th, 2009, 10:16 PM
Infinity cannot be reached or else it wouldn't be the true concept of infinity. This concept was only given a name because it appears often and had a need to be identified. Much like the square root of -1 was given the identity "i" though it is technically impossible.

In short, infinity is indeed a concept and not an actual number.

To understand it, I think about dividing by zero. :D

February 7th, 2009, 10:18 PM
Infinity is everything and nothing. Because everything and nothing stretches on for infinity, profoundly.

If I had to choice a choice though, it'd be a concept.

February 7th, 2009, 10:29 PM
The Infinite Hotel is a fun paradox. (http://scidiv.bcc.ctc.edu/MATH/InfiniteHotel.html) My Calculus prof told us that after class the other week. He said if you can understand that, you understand infinity. That was the best version I could find online without trying to remember it myself and getting it wrong.

At any rate, mathematically, infinity doesn't really exist. You can argue it in a few contexts but for the most part, if you've got infinity, you've got no real solution. As a concept, yeah it's definitely in existence. It's important as a concept because whether or not it's defined, it's imperative to have in a lot of math.

I try not to think too much on it. It hurts after a while. ;p

February 7th, 2009, 10:49 PM
Considering that infinity can't be used in arithmetic (infinity plus one or minus one is still infinity), I tend to think that it's a concept. One important thing to remember, though, is that there are rational and irrational numbers. One is a rational number, but pi is not. It's impossible to exactly represent pi, because it supposedly extends infinitely without repeating.

February 8th, 2009, 02:02 AM
My idea of infinity is something that can't be defined. For some reason whenever I think about it I always imagine something divided by zero. Maybe thats just my representation of it. Even though it isn't a number its still used in Mathematics, though, the only application I can think of on the top of my head is in limits.

I think the question is whether infinity is more useful as a number (acting like one anyway) or as a concept. Infinity is incredibly useful as a number, without it we wouldn't have Calculus. I'm not sure how infinity is used as a concept. I've thought about it a few times but I've never done any research because it seems like one of those things we can come close to understanding but will never fully understand. I suppose its used to describe things in Philosophy? I'm not sure, I don't feel comfortable commenting without any knowledge on it.

February 8th, 2009, 02:24 AM
I don't believe it is a number, because it never ends. That's all.

Dr Helios
February 8th, 2009, 02:29 AM
Infinity is a concept, but a concept that must exist, as x÷0=∞. It's like pi, although pi must exist, because c÷d=π, it can never be fully written out by humans or computers.

Although, that's just what went around in my brain, I don't have much 'real' knowledge about it.

February 8th, 2009, 04:53 AM
We covered the concept of infinity in Philosophy, specifically the Kalam argument. It states that a true infinity cannot exist, due to the fact that, as previously stated, infinity plus one is equal to infinity. We were given a simple example to Lightning's Infinite Hotel - the example of the Infinite Library. It states that there are an infinite number of books in a library, half red and half black. The red books are removed, with a number of black books left. However, there are still infinity black books left, and thus ∞/2=∞. Thus, infinity is simply a concept, and does not truly exist. The comparisons to pi are rather pointless, as pi has a value (albeit with tens of thousands of digits after the decimal point), whereas infinity does not - Hallucination's comparison to i was more valid.

(The Kalam argument goes on to state that because of this the Universe cannot have existed infinitely, and thus there must have been a series of causes caused by a First Cause, generally attributed to God. But that's for another time.)

February 8th, 2009, 06:08 AM
Eight million is the number that traditionally represents infinity, in Japan at least.

It is a concept obviously but I would say it doesn't exist in the real world — everything serves its term and comes to an end. Assuming commonly acknowledged science is correct, even the universe is not infinite since it is expanding, and so must be a finite mass.
Time is the only infinite thing IMO, but then that is also a concept to me so whether it is infinite or not it's not part of the real world and so not relevent.

February 8th, 2009, 06:13 AM
"Finite" means limited, whereas "INfinite" means unlimited, or having no boundary or end. Therefore nothing can count to infinity, making it more of a concept than a true number.

February 8th, 2009, 10:33 AM
Infinity actually has to be a concept, even though an equation reaches it:


As someone else already stated it.

How many times does 0 fit into x if x>0 and real?

However, there is a controversy if we invert the equation:


That is not true. Any monkey in 3rd grade can tell anything times 0 is 0.


∞ does not follow the rules that any real number follows. Thus, it cannot be a number.

viridian doubletongue
February 8th, 2009, 11:04 AM
It's a hypothetical value.

February 8th, 2009, 11:08 AM
It is a concept of something that never end.

February 9th, 2009, 07:07 AM
Infinity is both, depends on the perception. If you're talking mathematically, it's a value that has no end, positively or negatively. Otherwise, it's a scientific concept of an endless time.