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Physics, Astronomy & Cosmology / Re: Do we go round in circles?
« on: 10/08/2019 14:16:49 »I’ve put together a few questions, and made some tentative moves towards possible answers, or where they might be found. Still a long way to go, but comments would be appreciated.I put in some comments, but have not read the whole thread.
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1. If infinity is not a number, how can you subtract anything from it?It isn't meaningful to subtract a number from a not-a-number. 'Infinity' is more of an adjective, meaning 'without limit'. Much confusion arises when its syntactic usage as a noun leads one to treat it as a number.
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2. If the Universe is infinite, it contains an infinite number of galaxies. How does one define an infinite number?Again, it simply means there is no limit to the number of galaxies.
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3. If one is subtracted from an infinite number of objects, is the remainder still an infinite number? If not, what is it?Per point 1, it is not meaningful to do addition and subtraction with 'without limit'.
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4. Would an infinite number of (identical) objects contain all the examples of that object that could exist?If they're identical, how is it not one object? This sort of gets into the law of identity.
Perhaps you mean something like 'just because there are infinite points along a line doesn't mean that there are not other points that do not fall on that line. So there are examples of points not in that set, but I'd not call any of the points 'identical' since they're all at different places on the line.
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5 Is “absolute infinity” (sensu, Cantor) amenable to mathematical manipulation?Since it isn't a number, not sure what you're asking. It's expressed as Ω, but that's not your question. One infinity isn't larger than another since they're not numbers. Perhaps it means 'highest cardinality', but cardinality isn't an expression of the magnitude of something. Only numbers have magnitude.
6.Quote from: WikiThe Absolute Infinite (symbol: Ω) is an extension of the idea of infinity proposed by mathematician Georg Cantor.
It can be thought as a number which is bigger than any conceivable or inconceivable quantity, either finite or transfinite.
How could this concept be expressed without referring to infinity as “a number”?
I'd not trust wiki on this. They call it a number, but any number is finite. I think a proper mathematician would not word the description this way.
Since nobody replied to this, I'll just say that the mean density of matter in the universe is typically presumed to be the same as it is in the parts we see (cosmological principle). yor-on's statement would only apply to a model where there is infinite space, but there is finite matter, presumably all clumped nearby. I know of no such model that is seriously considered.Quote from: yor_onAn infinite universe is possible only if the mean density of matter in the universe vanishes.
Why? Simple explanation, please.
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I'd really appreciate some guidance with #23. I'm trying to tie up loose ends.
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