Multiple infinities
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14-09-2013, 08:30 AM
RE: Multiple infinities
I have been counting them.

Sadly I lost count at around 65,734,823,445,910,066,773,666,217,953,9865.00567 Undecided

For no matter how much I use these symbols, to describe symptoms of my existence.
You are your own emphasis.
So I say nothing.

-Bemore.
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14-09-2013, 08:31 AM
RE: Multiple infinities
An infinity of rational numbers exist between 1 and 2. A second infinity exist between 2 and 3, and so on and so forth an infinite number of times. Interestingly both infinities can be considered the "same" and the infinity that contains all of them can also be considered the "same" because they are both countably infinite... but that's another story.

As to whether any infinity can physically exist within the universe, that's not known. We use a mathematical technique called calculus to describe many physical phenomenon. That technique breaks a thing down into an infinite number of parts to describe how it behaves as a whole... but calculus does not accurately explain some of the finest features of the universe precisely because those features don't break down infinitely. Fluids break down into molecules and atoms. Fundamental forces break down into quanta, etc.

So yes in principle, mathematically, many infinities can sit alongside each other. Infinite doesn't mean "contains everything", just "contains an uncountably many number of things" while another uncountably many things may exist outside of that set. Physically, none has been observed so far to my knowledge. If you're looking for a term for "contains everything" the word is "universe", not "infinity".

Give me your argument in the form of a published paper, and then we can start to talk.
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14-09-2013, 08:50 AM
 
RE: Multiple infinities
(14-09-2013 08:31 AM)Hafnof Wrote:  An infinity of rational numbers exist between 1 and 2. A second infinity exist between 2 and 3, and so on and so forth an infinite number of times. Interestingly both infinities can be considered the "same" and the infinity that contains all of them can also be considered the "same" because they are both countably infinite... but that's another story.

As to whether any infinity can physically exist within the universe, that's not known. We use a mathematical technique called calculus to describe many physical phenomenon. That technique breaks a thing down into an infinite number of parts to describe how it behaves as a whole... but calculus does not accurately explain some of the finest features of the universe precisely because those features don't break down infinitely. Fluids break down into molecules and atoms. Fundamental forces break down into quanta, etc.

So yes in principle, mathematically, many infinities can sit alongside each other. Infinite doesn't mean "contains everything", just "contains an uncountably many number of things" while another uncountably many things may exist outside of that set. Physically, none has been observed so far to my knowledge. If you're looking for a term for "contains everything" the word is "universe", not "infinity".

Well if it's based on the Big Bang theory, we can conclude, maybe the Universe is finite and limited in size. But if the Universe is indeed limited and finite in size, then what's "beyond" the Universe? Maybe what's "beyond" the Universe is the same as the "state" prior to the Big Bang but who knows? But in my opinion the Universe have no "beyond".
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14-09-2013, 02:04 PM
RE: Multiple infinities
(14-09-2013 08:31 AM)Hafnof Wrote:  An infinity of rational numbers exist between 1 and 2. A second infinity exist between 2 and 3, and so on and so forth an infinite number of times. Interestingly both infinities can be considered the "same" and the infinity that contains all of them can also be considered the "same" because they are both countably infinite... but that's another story.

As to whether any infinity can physically exist within the universe, that's not known. We use a mathematical technique called calculus to describe many physical phenomenon. That technique breaks a thing down into an infinite number of parts to describe how it behaves as a whole... but calculus does not accurately explain some of the finest features of the universe precisely because those features don't break down infinitely. Fluids break down into molecules and atoms. Fundamental forces break down into quanta, etc.

So yes in principle, mathematically, many infinities can sit alongside each other. Infinite doesn't mean "contains everything", just "contains an uncountably many number of things" while another uncountably many things may exist outside of that set. Physically, none has been observed so far to my knowledge. If you're looking for a term for "contains everything" the word is "universe", not "infinity".

The infinite I think Mike is referring to is the idea that comes up in debate topics from time to time regarding religion. The theologian often likes to discount anything in physical reality being infinite in order to justify god somehow was necessary to get things going. Infinity as a concept exists, and since Math is just logic, mathematical infinity is just a concept. But is there such a thing as infinity in the physical world? The concept of god can exist even if god doesn't actually exist. So just because we can conceive of infinity, doesn't mean it exists.

There may be infinite set of numbers between any two integers, but in the physical world we live in, it may be that there are not an infinite number of positions in space-time between two points. And it may not in fact be possible to go out at some distance into infinity if the extent of the universe is finite.

In the theological debate, though, I think whether there is an infinity or not is not particularly relevant to the point theists want to make when they assert there is no physical infinity. They make this assertion to defend the idea that everything has to have a beginning and there fore, there is a first cause, and by the way, that first cause is god who apparently can be infinite. If the universe can cause itself as suggested by some Physicists, then we really don't need our universe to exist within something that is infinite.
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