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niceatheist
Guest
I didn’t say a closed manifold is infinite. Quite the opposite; a closed manifold is finite, and yet has no boundary. That’s why a lot of models of the universe, or at least the observable universe, view it as a closed manifold. The point being that, at least for most cosmologists, the universe is not infinite, but neither does it have an “edge”, and quite possibly neither does it have a starting point (if you extend the concept of a closed manifold to encompass time as well as space). That so far as I understand is what Hawking and other cosmologists invoking “imaginary time” (which is not imaginary in the sense of being made up but is imaginary in the sense of imaginary numbers); time itself curves back (like a circle) and the curve may become infinite but never actually has a beginning.To me that is all infinite is, something without a defined end point. You’ll have to tell me more about how something can have a finite size and not have a defined boundary and can still be labeled as infinite. To me, currently, something with a restricted boundary is by definition not infinite. We may not have discovered the boundary yet, but we do not believe it is an infinite boundary. Such as counting to 10 but we can only discover 1-8 so far. Seems we are just talking about the definition of terms of the abstract though and those conversations are just fun for practicing logic.