(February 13, 2018 at 7:47 pm)Grandizer Wrote:Of course comparing the existence to a hotel is just silly(February 13, 2018 at 5:16 pm)RoadRunner79 Wrote: 1.) It is unbound by definition, you can't have it complete and thus bound. An actual infinity keeps going and going with more to go after that. It doesn't finish, hence an infinity
Let me just focus on this one for now, because I feel like this is your biggest hurdle.
Complete doesn't imply bounds. Hilbert's hotel was fully occupied, but it doesn't mean that there were limited number of rooms. It just means that, because it had infinite number of rooms, guests were able to [simultaneously] exit their room and each move to the next one, no problem. If there had been a block at the end, then it wouldn't be an infinite number of rooms. It would be a finite number of rooms.
About Zeno's paradox and infinite divisibility, a general question for all: would it be reasonable to argue that what works on paper does not necessarily translate effectively to the real because mathematics doesn't suffer the constraints reality (or at least this local universe) tends to have, IF motion were to be defined classically and A-theory of time assumed? In the abstract world of mathematics, everything is static and lines are abstractly perfect even if, in the real world, they are not drawn perfectly. But in this universe at least, it does seem like Zeno's paradox may be pointing to a quantized universe in terms of space divisibility and in terms of time (so discrete rather than continuous)?
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