kwigibo

OK, a bit of armchair philosophy. How can 'space' be anything but infinitely big in size. even if you limit space, what is beyond the limit? if the answer is nothing than that is still 'space', so it's not a limit at all, and if there is something beyond that limit, than it's still not a limit. So i guess the question i am asking is how can you limit the universe? even if there is finite matter, how can it possibly exist in a finite space?

Adrian Selby

"If all possible moments exist and no others can be added then there is a finite number of moments. "

But if all possible moments defines an infinite set none could be added because you cannot add to an infinite number, its already infinite.

Adrian

Koyaanisqatsi

What she said!

Draygomb

No. Infinity + 1 = Infinity
Static sets are finite.

Any point at which you stop adding to (or subtracting from) a set the set becomes finite.

Jonsey3333

kwigibo:
OK, a bit of armchair philosophy. How can 'space' be anything but infinitely big in size. even if you limit space, what is beyond the limit?

Jonsey3333:
You fall off the side of the universe. Duh.
<a href="http://www.flat-earth.org/society/" target="_blank">Flat Earth Society</a>

- Mike

Theophage

To clear up a few misconceptions:

No. If the rules of cause and effect in that universe are such that no chain of events possible from X can produce Y, combination Y will never occur again once X has occurred.

Dray actually got this one right, you can keep adding to an infinite set. As an example, take the set of even numbers; an infinite set, yes? Now start adding odd numbers to it: 1, 3, 5, etc. You still have an infinite set, but you've added elements it didn't have before.

Adrian Selby

Hmm, I'm almost certainly showing my ignorance here, but I'm open to being put right.

Infinity+1=Infinity

Why can't infinity only be equal to itself, and if there is infinity, if one is able to add 1 to it, it couldn't have been infinity, because it was less than when the 1 was added.

I'm not sure how a 'set' can contain anything infinite. I suppose if one described the set of all possible numbers as an infinite set, I would want to look more closely at whether there's a difference between 'all possible numbers' and 'infinite numbers'. It appears that when the words all possible numbes are used, it can be described as a set. But when I say 'a set containing an infinite amount of numbers' I don't feel comfortable saying it, as vague as that is, because I would automatically frown at what such a phrase could mean.

Do you see a distinction between 'infinite numbers' and 'all possible numbers'? Or is it the case that if they're identical in meaning, it wouldn't make sense to talk of a 'set' of infinite numbers/all possible numbers.

Adrian

Francois Tremblay

If I remember my physics classes correctly, space is limited and unbounded.

It is a bit misleading to talk about bounds of the universe, since the universe does not "expand" as such - there is nothing for it to expand in. But I suppose it's a good analogy. Imagine the universe as the flat surface of a balloon that keeps inflating.

Draygomb

If you go straight forward far enough you will end up right where you were.

Adrian
You've noticed the problem with infinites, they don't make sense. Infinity - Infinity can = Infinity or Zero or Negative Infinity and still be right.

Theo But that doesn't stop A and B from reoccuring constantly.

[ January 31, 2002: Message edited by: Draygomb ]</p>

CardinalMan

Keep in mind that there are different sizes of infinity (there are more real numbers than natural numbers for example). In mathematics, each set is assigned a certain cardinal number, which represents just how big the set is. It turns out that the sets {...,-2,-1,0,1,2,...} and {0,1,2,...} have the same infinite size (you can pair off the elements), and so they are assigned the same cardinal number, which is usually called aleph_0. Now one can define addition, multiplication, and exponentiation of cardinal numbers so that it makes sense to ask what the values of aleph_0 + aleph_0 and aleph_0 * aleph_0 are. The real numbers are bigger than the natural numbers (you can not pair off the real numbers with the natural numbers), and have size 2^(aleph_0) (that is, 2 raised to the aleph_0 power).

When properly defined in mathematics (and not used in same vague imprecise philosophical way), the concept of infinity makes just as much sense as any other branch of mathematics. There are precise definitions for how to add, multiply, and exponentiate ordinal and cardinal numbers as discussed above (although subtraction may not be well-defined in the usual sense). I strongly urge everyone here to learn some serious set theory before making wild philosophical claims about what can and can't be done mathematically with infinity.

CardinalMan