Our universe is not infinite, It is expanding which pretty much sums up that it has a current size.
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Still there are things that are provably infinite. The square root of two for example can be shown to have an infinite description even though it can be known to an arbitrary precision.
These two statements are seemingly in conflict. Imagine doing the opposite and squaring two (and each subsequent iteration) at a faster rate than the universe is expanding. Now, imagine that the manifestation of the ever-increasing numbers are physical numbers with a physical size. At some point, the physical size of the numbers would fill up the universe. Where would the overflow go, assuming that you continue the process of squaring each new iteration and the results cannot be compressed within the universe?
My initial point in my previous post wasn't really that the universe is infinite -- I recognize that it is expanding -- but, rather, what exists beyond the edge? Whatever is there, if we travel to its opposite edge, what is there, etc.?
So, a foam (which is entirely hypothetical) could have a definite size and yet contain an infinite number of "bubbles". And yes, multiple dimensions are also hard to visualize. I personally try to image the projection of the dimensions on our discernable space-time paradigm. That is to say, I can't see them all at once, but I can sometimes see (in my mind) the interaction of some on our version of space-time.
I generally agree. It's sort of like the paradox of walking toward a wall (the distance between you and wall is finite) and constantly halving your speed as you approach, so you never reach the wall despite always moving toward it.
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