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[Japo]

Originally Posted by _r.u.s.s.

well, it's a set, which has infinite ammount of numbers, so..

No, infinity isn't certainly a set, it's not the whole field of real numbers --and it's none of them either. Infinity could be thought of as a single number two numbers (plus and minus infinity, although with complex limits it's different), but it's actually a concept that appears only when talking about limits, so everybody misunderstands infinity as a mathematical concept or number.

Originally Posted by AlumiuN

That's only theoretical -> e.g. 1 is the sum to infinity of that sequence, just in one step. In what could be called 'practical terms' e.g. no theoretical numbers such as infinity, Achilles will never pass the tortoise. Of course, taking exact points in time for a continuous scale doesn't have any bearing in real life, but from the standpoint of conventional maths, 1 is never reached.

But it was you (or Zeno) who broke up whatever into infinite parts for no good reason. Everything can be broken up into infinite parts. You can be thought of as made up of infinite hypothetical parts, then it must mean that you cannot exist or that you cannot be contained or something stupid.

You can calculate how and when Achilles will pass the tortoise without contemplating any infinite sequence, just in one step. The fact is however that if you insist on calculating the time for each of the infinite time spans and add them up, you get the same result. BTW that is what maths is about, you always get the same result, the true result, no matter how. Very unlike speculation, or so-called "philosophy".

Arguing philosophically against something proven by maths or experience is a sure way to embarrass oneself... And I will henceforth stay away from the philosophical side of this topic, since philosophy = pseudo-science. :amused:

[sgtboat]

I think one is the biggest number. AS the wizard in the movie fable showed us all the power in the world is concentrated in the oneness aspect of oneself. That makes one a really big number if you measure the effect of one person on the course of society.

[_r.u.s.s.]

Originally Posted by Japofran

No, infinity isn't certainly a set, it's not the whole field of real numbers --and it's none of them either. Infinity could be thought of as a single number two numbers (plus and minus infinity, although with complex limits it's different), but it's actually a concept that appears only when talking about limits, so everybody misunderstands infinity as a mathematical concept or number.

first of all, nobody said that infinity is a number (?). and then, infinity can be as well declared as a set with infinite amount of objects

[Tomekk]

Here, we will never have the chance to what the biggest number in the world is, cause it goes on forever....

[Japo]

Originally Posted by _r.u.s.s.

infinity can be as well declared as a set with infinite amount of objects

You already said that but I'm afraid I don't follow...

Not the mathematical "infinity" usually represented by

As in, "Achilles must traverse an infinite number of points before catching up to the tortoise", or in, "when x tends to 0, 1/x² tends to infinity". I think that's what we were talking about.

[Romano]

Originally Posted by Japofran

You already said that but I'm afraid I don't follow...

Not the mathematical "infinity" usually represented by

As in, "when x tends to 0, 1/x² tends to infinity".

Maybe to consult: http://en.wikipedia.org/wiki/Democritus

[_r.u.s.s.]

japorfan infinity is not only used or defined in function limits=S

[dosraider]

When I was still maried, and came home drunk after a drinking party with friends.
Infinity:
My wife nagging, and nagging , and nagging, and nagging, and nagging , and nagging, and nagging, and nagging , and nagging, and nagging, and nagging , and nagging, and nagging....

[DoomYoshi]

Big fleas have little fleas upon their backs to bite them
Little fleas have smaller fleas and so on ad infinitum

Is there really such a thing as "infinity"?

It's a tough question, because the word "infinity" can mean different things in different contexts. In mathematics, whether or not a certain concept exists can depend on the context in which you ask the question. If you want to know more about this, you can refer to a fuller explanation of how a mathematical concept can exist in some contexts but not in others.
Here are some of the contexts in which the question "is there such a thing as infinity" can be asked, and the answers appropriate for each context. The details are given afterwards.

1. In the context of a number system,
   in which "infinity" would mean something one can treat like a number. In this context, infinity does not exist.
2. In the context of a topological space,
   in which "infinity" would mean something that certain sequences of numbers converge to. In this context, infinity does exist.
3. In the context of measuring sizes of sets,
   in which "infinity" means a measurement of the size of an infinite set. In this context, such "infinity" concepts do exist but there are more than one of them, since not all infinite sets have the same size. So there does not exist any one single "infinity" concept; instead, there exists a whole collection of things called "infinite cardinal numbers".

I feel the need to present some sort of consensus. This is how it is done at my school (University of Toronto).

[_r.u.s.s.]

what you posted is already here in this thread