I would agree with that
I guess, although I don't know if what I would mean by "closed system" is the same thing that anyone else would mean.
I don't know the answer to the question, but is there a difference between the vacuum of space and space itself?
I'm not sure how to take that. I don't think the nature of numbers in and of themselves tell us anything about the universe. Numbers are abstract things that we have created in our brains. Now, why did we create these particular abstract objects, rather than some others? We live in the universe and observe various physical phenomena around us, so we have a tendency to create abstract objects that are useful for modelling the real objects. So maybe they are informative in that sense. But as for something quantifiable being infinite, do you simply mean that "quantifiable" means a (finite) number can be associated with it, so it must not be infinite? If so, then that would be tautological. (So I would agree)
I don't know what it means to be qualitatively infinite, but I do think I know what it means to be quantitatively infinite - larger than any finite quantity. So I think the universe could conceivably be infinite in that sense, which would mean the size of the universe is larger than any finite quantity. Whether that is actually the case, I do not know.
I don't think you are alone on that. As I understand it, the singularity is what happens if we take the laws of physics as we know them, look at the universe, and try to figure out what it looked like some time ago. However, our understanding of the laws of physics is incomplete at best (and wrong at worst), and before we get back to the singularity, we encounter a situation in which our understanding of the laws of physics begins to fail.
So I think the current answer on whether there actually was a singularity is, nobody really knows for sure. Perhaps a more knowledgeable person will disagree in the posts you find below this one![]()



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