# Yet another infinity problem

1. Sep 20, 2007

### LT07

Spare me the ridicule for asking a stupid question, I'm just your average guy trying to comprehend his environment. I do my best to understand the origins and workings of the universe but no matter what path I take I will end up facing an infinity of one form or other.

Ok here goes.

I have always assumed that it is impossible to have two infinitely sized objects since each would occupy space that the other should be existing in. If any infinite sized object ever existed then it would consume all 3D space and there would be no room for anything else to exist.

Now I'm not so sure.

I assume that 3D space is infinite in all directions.

Floating around in this space is a hosepipe of infinite length (infinite to the point it has no ends)

If its infinite in length then it can hold an infinite volume of water.

Any infinite volume should consume all of space but now I find I can have an infinite number of infinite volumes in an infinite amount of space.

It also occurs to me that I can walk up to the hosepipe and cut it in half creating a different type of infinite length, before it had no beginning or end and now I have two infinite lengths both with a beginning but no end.

Am I barking up the wrong tree, should I stick to my idea that an infinitely sized object is impossible or does an infinite amount of space allow for an infinite number of infinitely sized objects?

Don't blame me for asking such stupid questions I'm not the one dumping singularities all over the universe.

2. Sep 20, 2007

### pervect

Staff Emeritus

The situtation with infinite space is similar - an infinite set can have subsets that are the same size (i.e. can be put into a 1:1 correspondence with) the original set.

3. Sep 20, 2007

### LT07

Thank you for the reply, yes I have read that particular paradox but am still no closer to understanding infinity. The hosepipe being cut in half has just thrown further confusion at me. I can cut it in half once but never again, it has no middle that I can reach, all I can do now is cut off finite lengths.

So confusing.

4. Sep 20, 2007

### Hurkyl

Staff Emeritus
This is clearly false, as your counterexample demonstrates.

(I assume by "size", you mean volume)

5. Sep 20, 2007

### LT07

Yes I mean that an infinitely sized object would have infinite volume, however the hose pipe is not of infinite size (only length) yet by my reckoning it contains an infinite volume of water.

Something is desperately wrong with the way I perceive infinity.

6. Sep 21, 2007

### Hurkyl

Staff Emeritus
If you are not using "size" as a synonym for volume, then please explain what you mean by that word.

Also, you seem to suggest that the hosepipe doesn't have infinite volume; why do you think that?

Last edited: Sep 21, 2007
7. Sep 21, 2007

### TR345

Hmm. Is 2i>i? That is a tough one. I guess if you are talking about two infinite spaces, then they are both part of the same infinate space, so 2 infinate spaces can't exist because in the case of infinite space, there are no spaces only one infinite space.

As for the hose idea, I don't know what to say. I guess you could have infinite amounts of different objects and objects could be less frequently, or less densely organised through an infinite space.

If space and time are infinite, then maybe ultimately their is only one fundimental thing that makes up everthing and it is infinite in amount and all things and spaces are a part of it in its' infiniteness.

8. Sep 21, 2007

### LT07

See note in first post about average guy, the average guy is pretty stupid.

Yes I equate size to be the same thing as volume, that is anything with size has volume! clearly this is something I need to read up on as you seem to know something I don't. I can imagine something like a flat sheet with no thickness but has width and height, it could have a surface area but no volume.

As for whether the hosepipe has infinite volume is the thing I'm trying to understand, if its infinite in length then it must contain an infinite volume of water, but if the volume of water is infinite then how come its not occupying all of space?

I have always considered that something of infinite volume must occupy all available space. I hardly understand the question never mind the answer. :)

9. Oct 2, 2007

### Feonix12

You cannot have an infinite number of infinitely sized objects. Why? Because if there were infinite number of atoms to create these objects then there would be no space in the universe. There is a limited number of atoms in the universe, even though its a bigger number then we can ever comprehend.

10. Oct 2, 2007

### Hurkyl

Staff Emeritus
Why would you think that?

Or that?

11. Oct 2, 2007

### Feonix12

If you believe in the big bang theory...
If there was an infinite number of atoms then we couldnt move or exist in the first place. At night when you look up in the sky and see all that blackness, thats empty space. If there were infinite atoms to occupy the universe there would be no blackness, there would be nothing except a solid object, atoms touching atoms throughout the entire universe. Take snow for a rough example, when its falling from the sky you can see inbetween each snowflake, there's space between them(dont get technical with me about gases and particals), but when it compresses on the ground its just a solid hunk of snow. If you believe in the big bang theory then there is no way in hell there are infinite number of atoms, and there is not infinite energy to be consumed. Sure we can harness chemical reactions and keep energy going indefinetly, but fact is we wont be able to keep that reaction going indefinetly in the first place, the sun will colapse on itself some year. All the suns will, or will be engolfed within black holes and the black holes will eventually eat eachother up. Then supposedly explode again like another "big bang". This reaction keeps going forever. Just my theory on OUR universe. Thats not including parallel universes or other dimentions. Everything basicly boils down to me as everything is balanced, for every action there is a reaction, + -.

Damn i spew alot of crap out.

12. Oct 2, 2007

### TR345

Your reasoning involves infinate objects in finite space. How could infinate space be full? There can be no max capacity because there is infine room, never ending. If this space never ends, and there is a snowflake every two inches, then mathematically there is still infanite snowflakes.

13. Oct 2, 2007

### TR345

Besides this is a hypothetical question. The hypothetical isn't: If the big bang theory is true, then could there be infinate objects in an infinate space? Big bang theory cannot rule out infinate space anyways. There could be an infinate amount of big bangs and an infinate amount of universes for all we know.

14. Oct 2, 2007

### JesseM

Actually, the basic Big Bang model already assumes that space would be infinite if the density of matter is at or below a certain critical value known as Omega--you don't need an infinite number of Big Bangs, just the one is enough. See my last post (#8) on this thread.

15. Oct 3, 2007

### Feonix12

Ummm i dont know how you interperated my posts as but i never ment it to apear as my reasoning involved infinite objects in finite space. It was Finite objects in infinite space.
And if there was a snowflake every two inches spanning accross the infinity of space then you would still have a 2 inch gap were more snowflakes COULD be. This just goes into a big mess because if you can have MORE than infinity it wasnt infinity to begin with which is why it supports there is not a infinite amount of atoms to fill the universe. Its like saying Infinity + Infinity. double infinity? no

Last edited: Oct 3, 2007
16. Oct 3, 2007

### TR345

I'm just saying that mathematically there would still be infinate snowflakes. I'm not saying that makes sense. All your saying is that it doesn't make sense to you. So maybe you ought to not believe in an infinate space.

17. Oct 3, 2007

### Feonix12

It dosnt make sense to anyone, nobody knows any of these idea's. I thought/think that all matter came/comes from the big bang theory and the "dark universe" was already there before this event.

18. Oct 3, 2007

### Chronos

I'm surprised no mention has been made of Olber's Paradox. The universe cannot be infinitely large, old, and homogenous.

Last edited: Oct 3, 2007
19. Oct 3, 2007

### Garth

Actually the universe cannot be both infinitely large and old and also static if the sky is dark at night.

The red shift of light from distant stars in an expanding and infinitely large and old universe may be enough to attenuate the light flux below observable limits.

Garth

20. Oct 3, 2007

### JesseM

How is it relevant that you'd have gaps where more snowflakes "could" be? The universe has no obligation to fill up all of space, in the real world we can see that there is a certain density of hydrogen atoms even in deep space, so there's plenty of empty space where more hydrogen atoms could be, but aren't. There is nothing illogical or contradictory about the idea that the universe continues on this way forever, giving you an infinite number of hydrogen atoms but plenty of empty space, with a similar average density everywhere.

If you think there's something mathematically impossible about the idea that you can add to infinity and still get infinity, you're wrong. For example, the number of odd numbers is infinite, and the number of odd+even numbers is also infinite.

Last edited: Oct 3, 2007