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We don't know 🤷
One of many remaining mysteries of the universe is what expansion really means. We can measure that it is indeed expanding, but we don't know what's driving the expansion (other than "dark energy" which is actually only a placeholder in equations). We also have no idea about the size of the universe. Observable universe is just that - as far as we can see. But there is more beyond that we can't see. There is no observable border to it, but we also can't claim it's infinite because there is a lot of proof for expansion.
Why does infinity rule out expansion?
I don't think it does. At least in mathematical sense.... Something can be infinite and growing. But it's been a long time since school so I may be off with my language.
I am not a mathematician so I am not able to well explain this concept, but there are different sizes infinities. "Infinity" is not one thing.
But there are infinite sets that contain infinite sets, so therefore there are infinities that are larger than other infinities.
It is possible that the infinite universe is expanding into another, larger, infinite space.
Or really anything is possible, we don't know.
Numberphile has a pretty good video on different sized infinities. Newpipe is bugging out lately so I can't dig up the video but if you're interested you should be able to find it easily enough
Yes exactly. What you're describing is cardinality. For example the number of natural numbers (counting numbers) is a smaller infinity than the number of real numbers (rational numbers + irrational numbers).
This can be proven rigorously.
I don't think it's even set in stone that we are expanding at all. There is another theory that the universe as we know it could be the inside of a black hole. In this scenario we could actually be shrinking instead - or rather being compressed, if that makes sense.
I think it's pretty well established through empirical observation that the universe is expanding, based on all our current understanding of the universe. We don't know WHY, and we don't understand how, but it's not really under debate at this point as a fact.
What happens inside a black hole is entirely and utterly unknown, and it's such a crazy mind bending concept that anything we theorize is as close to informed speculation as you might get.
I'd heavily take with a grain of salt anything that replaces something we know as well as you can observe with a theory that goes something like "well maybe we're inside a black hole."