RE: Why the universe is most likely not infinite – Part 8: Does the second earth paradox rule out infinity?
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Well, I think there's a hole in the second Earth paradox. For example, we can have an infinite range of numbers without any two numbers being 100% identical. I think same can apply to cosmic structures, they can be infinite without any being 100% similar.
Also since it takes time for these cosmic structures to form, it would mean that for an infinite universe to exist, it must have existed an infinite length of time. A universe that began at a certain point in time, whose age is not infinite, cannot be infinite in size, since it takes time for it to form.
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Good point, infinite resolution of spacetime would indeed be a counter argument for the second earth paradox, but I doubt that we have infinite resolution, infinite range of numbers in the real world. Time is not such an issue for the second earth paradox, because it assumes an infinitely large universe were an infinite number of solar systems could form simultaneously.