How big is infinity?

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Smilin

Diamond Member
Mar 4, 2002
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You say you didn't pull a one from the end because there is no end and this proves that 1=2.

M'kay. I'll buy that 1=2 if you'll prove there is no end.

:D
 

Hazer

Member
Feb 16, 2003
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The different sizes of 'infinities' mostly deals with sets and series. But consider this: A set (or series) contains bounded information. Example, X={all integers}={1,2,3,4,5,...}. Y={all prime integers}={1,2,3,5,7,11,13,...}. Both sets go inot infinity. But if you took X, and removed Y from it, there would be less in X (but still going to infinity). If all infinities were equal, then setX minus setY would equal 0. But that is not really the case. And since what results from taking Y out of X leaves a set that is diminshed from what set X was, then how can that infinity be the same? This is the problem with working with sets and series.

To clarify what the meaning of infinity is, just think of something that goes on forever. Infinity means mostly to 'keep going'. There really is nothing equal to infinity. Most often, mathemtaics uses the term "as it goes to infinity". Not "when it equals infinity". Sets and series by concept mean something that is bounded. Even if the series has an infinite amount of possibilties, it is conceptually bounded by something :example: the set of integers.

Infinity is a concept. It is not a mathematical rule.
 

gururu

Platinum Member
Jul 16, 2002
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I completely agree with Hazer. Too often people fail to realize that mathematics and other sciences
are simply tools to better understand our environment or ideas. It is possible to understand how math
might be used to better understand infinity, but the application of math and its inherent restrictions must
also be understood, and in some cases, as I believe with infinity, math is inadequate. Not because math is
faulty, only because it is not perfect and infinity is.
 

ynotravid

Senior member
Jun 20, 2002
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Originally posted by: gururu
I completely agree with Hazer. Too often people fail to realize that mathematics and other sciences
are simply tools to better understand our environment or ideas. It is possible to understand how math
might be used to better understand infinity, but the application of math and its inherent restrictions must
also be understood, and in some cases, as I believe with infinity, math is inadequate. Not because math is
faulty, only because it is not perfect and infinity is.
Or at leaste modern math.
 

sao123

Lifer
May 27, 2002
12,653
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Sometimes I think that people try to breach the threshold between Applied Mathmatics, and Mathmatical theory.
They do not grasp the difference between the two as being "concrete" vs "abstract or conceptual"
The two are not interchangeable especially in a theoretical discussion as this, even though Abstract math is based on principles of concrete math.
 

Smilin

Diamond Member
Mar 4, 2002
7,357
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Don't forget things can be never-ending *without* being infinite as well. Our universe I think is a good example of this.
 

kylebisme

Diamond Member
Mar 25, 2000
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Originally posted by: ynotravidOr at leaste modern math.


even more than just modern, all we will ever have is human math. i don't recommend you hold you breath for perfection, a lot of people have already died doing just that. ;)

also, there very much are different sizes of infinity. it might be easier for some to understand it as "there are different densities of infinity" but it is the same thing in essence. to further elaborate; imagine you have an very simple universe which is nothing but pure water. knowing that water is one part oxygen and two parts hydrogen, it is obvious that the number of oxygen atoms is equal to the number of water molecules, and the number of hydrogen atoms is double that value. assuming this universe of water is infinite, then the number of water molecules, number of oxygen molecules and the number of hydrogen molecules are each equivalent to a value of infinity. however, this does not change the fact that there is twice as much hydrogen as there is oxygen in water, and hence we have an example of different sizes of infinity.


woops, i can't belive i did that. thank you for pointing it out gururu. ;)
 

gururu

Platinum Member
Jul 16, 2002
2,402
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i think you mean two hydrogen atoms per oxygen in a water molecule. :)
that's a nice analogy Snowman, and I've had a hard time thinking up an argument.:eek:
here goes...

if you had to buy each atom online in order to make an infinite amount of water molecules,
would you ask for twice as many hydrogens as oxygens or would you ask for an infinite amount of each?

I'd order the same amount.






 

Gururu is correct. But just to add to the imperfection of mathamatics theory, I too agree that math is not perfect, I remember my logic teacher telling us how when Set Theory was first invented people were hoping that this was going to be the perfection that would connect all math, but as the story goes, here comes whats-his-name's paradox that shows how Set theory doesn't cut it. Nevertheless I do belive that one day humanity will know the perfect unifying principals of math.