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My thinking is, your right, infinity can't be measured. Let me give an illustration of what I'm thinking. Say, in space (by space I mean an imaginary void, not real space), there's a road, who's size is infinite (NOT infitesimal), remember, infinity means "boundless", so the road's size wouldn't be bound, and without bound, things keep going. So while on the road, we take a measuring tape and measure part of the road we're standing on, which we measure to be... 42 inches. Now, if we want to, we can walk a few yards and measure the same length out again. How does that not prove that 42 is smaller than infinity? Now, let's say we can pick up the road. Now matter which way we place it, we won't be able to put it within the 42 inches we have measured out. How does that not prove that infinity is bigger than 42?
I didn't say it wasn't. I said it is also smaller than 42. It is both things at the same time in fact. Or more probably, neither one of them. It does not respect our puny attempts at giving it a dimensional property. If I tell you that I measured the distance between the arrow and the target as being 42 paces, won't you immediately reach the realization that infinity is after all also smaller than 42 paces?