Abge, maybe it is a question of definition? Could you define what you mean by infinity?

@fulhamish

Anything from here is fine: http://en.wikipedia.org/wiki/Infinity#Mathematics

@ful

Is your argument that we can't have an infinite amount of something irl? I agree; there aren't enough atoms. But, that doesn't mean we can't have infinite vacuum.

Putin writes:

It's easy to get confused because Wilberforce and his cronies established organizations with progressive sounding names like the "Abolition Society", but then when you dig deeper you see that they openly state that their mission is not to abolish slavery!

http://thesojournerproject.wordpress.com/2011/02/02/william-wilberforce-abolitionist-or-opportunist/

here is the author od the piece who informs us that she is currently applying for a post-graduate placement. I am sure that we all wish her the best of luck.
http://aconerlycoleman.wordpress.com/2011/08/27/musings-on-life-graduate-school-applications/

This gets more unfortunate each time I check one of Putin's references. I think that I had better stop now in the interests of decency.

@ abge

Let's go with the first sentence: a quantity without bound or end

Do you quantify the difference between 1 kg and infinity kg as infinity kg?
Do you quantify the difference between 1 000 kg and infinity kg as infinity kg?
Therefore after cancelling infinity does 1 kg = 1 000 kg?

I define an integer as a discrete number is this OK with you? i.e. -1, 0, 1, 2, 3, 4, 5 etc.
There are therefore, as you say an infinite number of them. We have an uncountable # of six packs and we have an uncountable # of cans. To say that uncountable times 6 tells us as much as uncountable times 6666666 or divided by 6666666 about the # of cans. That is precisely nothing.

(Incidentally, I have a feeling that the answer to the six pack issue lies in the application of mathematical set theory, but I am sure that you know more about this than me.)

Please don't misunderstand me I make no attack on maths in giving my views. I just question the application of the concept of infinity to matters of science where the ability to conduct repeatable measurement, both of integers and the appropriate units, must be paramount.

I don't know, fulhamish. I think you're not quite performing the right mathematical operations there. Sure, what you say would be true, except that nobody says you can subtract infinity from infinity and get zero. You might get anything. Even mathematicians realize this. After all, your kg example would create the same problem in pure mathematics as in physics, otherwise.

Also, there aren't uncountably many integers -- just countably many (which is still infinity).

It's true that there are unintuitive things about infinity so it requires special handling. I'm not sure why you can't still have a realization of it, though, after you've learned to handle it carefully.

Of course, I do agree that in actual measurement, infinity will never turn up, and this is perhaps your point. However, it can be very important in the theories we extrapolate from our measurements (quantum mechanics, e.g., couldn't get off the ground if it weren't for infinite-dimensional vector spaces).

@ful

"Do you quantify the difference between 1 kg and infinity kg as infinity kg?
Do you quantify the difference between 1 000 kg and infinity kg as infinity kg?
Therefore after cancelling infinity does 1 kg = 1 000 kg?"

No. This just doesn't make sense. You can't do these operations like this.

"We have an uncountable # of six packs and we have an uncountable # of cans."

Is it infinite =/= uncountable. That is why there are countable and uncountable infinite sets. This is an example of a countable infinite set.

" I just question the application of the concept of infinity to matters of science where the ability to conduct repeatable measurement, both of integers and the appropriate units, must be paramount."

There is a difference between what you is physically and theoretically possible to measure. Both are important to understand. If all physics was experimental, it would be very hard to understand the larger picture, that's why math is important.

And, I still don't see how any of this is relevant to your early comment about the universe.

@ semck, We agree then that infinity is not a number and therefore cannot be a measure of anything? It therefore must be defined as a non-empirical construct, albeit an extremely useful one?

@ Alligator, I would say that yes, if you can conceive that it exists, you should be open to the possibility, however slight. However, there's not time or energy enough to track down every possibility, so most of them we can safely ignore until such time as we are faced with the reality that one of them exists. God is knocking at your door, right now, and I'd say that the possibility that the God of the universe wants to talk with you on a personal basis is such a tremendous thing if it's true that we each need to fully investigate. People are telling you that they talk with God, that they have a relationship with God, that he deals directly with ordinary sinful people. Shouldn't you check it out??

@ful

Sure, but what's your point?

@ abge is your definition of infinity this -

''a quantity without bound or end'' or this ''uncountable''. Your and smeck's take on the matter only apply to the latter and not the former. That is why I asked you for your initial definition.

Infinite means different things depending on the context.

Well in that case it makes it all the more important to establish our terms of reference.

If we stick to our original definition ''a quantity without bound or end'', this would make ''theoretical'' sense.

"Do you quantify the difference between 1 kg and infinity kg as infinity kg?
Do you quantify the difference between 1 000 kg and infinity kg as infinity kg?
Therefore after cancelling infinity does 1 kg = 1 000 kg?"

No, you still can't do that because those are infinities of different size, so they will not cancel.

@abge
''Quantities without bound or end'' have different sizes? Man this is all very counter-intuitive.

Yes they do and yes it is.

Please skim http://en.wikipedia.org/wiki/Countable_set for clarification.

Actually, no, I'm sorry. Those two differences are the same size, but this is why you can't just subtract things from infinity like that.

@ abge
''Actually, no, I'm sorry. Those two differences are the same size, but this is why you can't just subtract things from infinity like that.''

So infinity is a completely abstract concept, any attempt to relate it to real numbers and their units is doomed to fail?

The punchline then must be how do we measure the age of an infinite universe without beginning? Certainly not in units of time be they seconds, years or Ma. To say that it is an infinite number of seconds, years or Ma old is therefore meaningless twaddle.

Yes, it does relate to real numbers. If there is a mapping between said infinite set and the natural numbers, it is countably infinite.

You seem to be having trouble with this concept. If the universe is infinite then we *don't* measure it.

Let me ask you a different question: How do we measure something smaller than the Planck Length? We don't. Does that mean nothing is that small? No.

Let me ask you a more relevant different question:

How far can you travel on a sphere? A infinite distance, no?

First, @ abg I know the quote itself is facesious, but I just wanted to use it after I saw it on your profile. ;)
Now, on the matter of infinity. Let's say you have 2 functions f(x)=3x+17 and g(x)=4x-13.
As x goes to infinity, both of these functions also trend to infinity. However, if you take h(x)=f(x)/g(x) Then h(x) trends towards 3/4 as x goes to infinity. This tells you quite simply, and usefully, that it asymptotically approaches 3/4.
That uses infinity to "measure" something, a ratio.

heh Yes, it is a pretty wonderful quote.

I agree with what you said, but I suspect it won't impress fulhamish, as there aren't such functions in reality. However, I still maintain that infinity is critically important for understanding how our universe operates.