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Infinity, Mathematics And Its Existence

TREssspa
Posts: 567
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2/7/2016 1:11:13 PM
Posted: 10 months ago
Is infinity used anywhere in mathematics?
Does it exist in reality?
Or. .. is it just imagination?

Can anyone here prove (or disprove) infinity?
Diqiucun_Cunmin
Posts: 2,710
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2/7/2016 2:35:22 PM
Posted: 10 months ago
At 2/7/2016 1:11:13 PM, TREssspa wrote:
Is infinity used anywhere in mathematics?
I've given you a list once, and I'll give it to you again.
-Domains and ranges of certain functions
-Defining asymptotes
-Infinite series
-Improper integrals
-By extension, defining probability density functions of continuous random variables
-The cardinality of the set of natural numbers, etc.

The list goes on.
Does it exist in reality?
Or. .. is it just imagination?
Infinity doesn't exist in reality in the sense that you can't find an infinite number of anything. This doesn't disprove its theoretical importance in mathematics.

'No one shall expel us from the Paradise that Cantor has created.' - David Hilbert
Can anyone here prove (or disprove) infinity?
The thing is, I hate relativism. I hate relativism more than I hate everything else, excepting, maybe, fibreglass powerboats... What it overlooks, to put it briefly and crudely, is the fixed structure of human nature. - Jerry Fodor

Don't be a stat cynic:
http://www.debate.org...

Response to conservative views on deforestation:
http://www.debate.org...

Topics I'd like to debate (not debating ATM): http://tinyurl.com...
Dirty.Harry
Posts: 1,585
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2/7/2016 3:58:21 PM
Posted: 10 months ago
At 2/7/2016 1:11:13 PM, TREssspa wrote:
Is infinity used anywhere in mathematics?
Does it exist in reality?
Or. .. is it just imagination?

Can anyone here prove (or disprove) infinity?

http://www.bbc.co.uk...
TREssspa
Posts: 567
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2/7/2016 3:58:37 PM
Posted: 10 months ago
At 2/7/2016 2:35:22 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 1:11:13 PM, TREssspa wrote:
Is infinity used anywhere in mathematics?
I've given you a list once, and I'll give it to you again.
-Domains and ranges of certain functions
-Defining asymptotes
-Infinite series
-Improper integrals
-By extension, defining probability density functions of continuous random variables
-The cardinality of the set of natural numbers, etc.

The list goes on.
Does it exist in reality?
Or. .. is it just imagination?
Infinity doesn't exist in reality in the sense that you can't find an infinite number of anything. This doesn't disprove its theoretical importance in mathematics.

'No one shall expel us from the Paradise that Cantor has created.' - David Hilbert
Can anyone here prove (or disprove) infinity?

any real application?
Diqiucun_Cunmin
Posts: 2,710
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2/7/2016 4:15:53 PM
Posted: 10 months ago
At 2/7/2016 3:58:37 PM, TREssspa wrote:
At 2/7/2016 2:35:22 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 1:11:13 PM, TREssspa wrote:
Is infinity used anywhere in mathematics?
I've given you a list once, and I'll give it to you again.
-Domains and ranges of certain functions
-Defining asymptotes
-Infinite series
-Improper integrals
-By extension, defining probability density functions of continuous random variables
-The cardinality of the set of natural numbers, etc.

The list goes on.
Does it exist in reality?
Or. .. is it just imagination?
Infinity doesn't exist in reality in the sense that you can't find an infinite number of anything. This doesn't disprove its theoretical importance in mathematics.

'No one shall expel us from the Paradise that Cantor has created.' - David Hilbert
Can anyone here prove (or disprove) infinity?

any real application?
Yeah, it might be more interesting to find a technical field that does not use calculus (which is, in a way, based on infinity) of any kind.

If you haven't noticed, I've already pointed out a 'real application': probability density functions, which make use of improper integrals. PDFs are important in statistics, which in turn is important in economics, actuarial sciences and other applications.

If you need more, calculus is important in calculating areas, volumes, velocities, lengths, and a variety of things that are essential in engineering applications.

I'm not sure if you'll believe me though: judging by your history on this site, you don't seem to be willing to re-evaluate your deeply-rooted beliefs.
The thing is, I hate relativism. I hate relativism more than I hate everything else, excepting, maybe, fibreglass powerboats... What it overlooks, to put it briefly and crudely, is the fixed structure of human nature. - Jerry Fodor

Don't be a stat cynic:
http://www.debate.org...

Response to conservative views on deforestation:
http://www.debate.org...

Topics I'd like to debate (not debating ATM): http://tinyurl.com...
TREssspa
Posts: 567
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2/7/2016 4:31:54 PM
Posted: 10 months ago
At 2/7/2016 4:15:53 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 3:58:37 PM, TREssspa wrote:
At 2/7/2016 2:35:22 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 1:11:13 PM, TREssspa wrote:
Is infinity used anywhere in mathematics?
I've given you a list once, and I'll give it to you again.
-Domains and ranges of certain functions
-Defining asymptotes
-Infinite series
-Improper integrals
-By extension, defining probability density functions of continuous random variables
-The cardinality of the set of natural numbers, etc.

The list goes on.
Does it exist in reality?
Or. .. is it just imagination?
Infinity doesn't exist in reality in the sense that you can't find an infinite number of anything. This doesn't disprove its theoretical importance in mathematics.

'No one shall expel us from the Paradise that Cantor has created.' - David Hilbert
Can anyone here prove (or disprove) infinity?

any real application?
Yeah, it might be more interesting to find a technical field that does not use calculus (which is, in a way, based on infinity) of any kind.

If you haven't noticed, I've already pointed out a 'real application': probability density functions, which make use of improper integrals. PDFs are important in statistics, which in turn is important in economics, actuarial sciences and other applications.

If you need more, calculus is important in calculating areas, volumes, velocities, lengths, and a variety of things that are essential in engineering applications.

I'm not sure if you'll believe me though: judging by your history on this site, you don't seem to be willing to re-evaluate your deeply-rooted beliefs.

Before you go on with these 'real applications' of yours, may I ask what is your definition of infinity?
Diqiucun_Cunmin
Posts: 2,710
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2/7/2016 4:38:32 PM
Posted: 10 months ago
At 2/7/2016 4:31:54 PM, TREssspa wrote:
At 2/7/2016 4:15:53 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 3:58:37 PM, TREssspa wrote:
At 2/7/2016 2:35:22 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 1:11:13 PM, TREssspa wrote:
Is infinity used anywhere in mathematics?
I've given you a list once, and I'll give it to you again.
-Domains and ranges of certain functions
-Defining asymptotes
-Infinite series
-Improper integrals
-By extension, defining probability density functions of continuous random variables
-The cardinality of the set of natural numbers, etc.

The list goes on.
Does it exist in reality?
Or. .. is it just imagination?
Infinity doesn't exist in reality in the sense that you can't find an infinite number of anything. This doesn't disprove its theoretical importance in mathematics.

'No one shall expel us from the Paradise that Cantor has created.' - David Hilbert
Can anyone here prove (or disprove) infinity?

any real application?
Yeah, it might be more interesting to find a technical field that does not use calculus (which is, in a way, based on infinity) of any kind.

If you haven't noticed, I've already pointed out a 'real application': probability density functions, which make use of improper integrals. PDFs are important in statistics, which in turn is important in economics, actuarial sciences and other applications.

If you need more, calculus is important in calculating areas, volumes, velocities, lengths, and a variety of things that are essential in engineering applications.

I'm not sure if you'll believe me though: judging by your history on this site, you don't seem to be willing to re-evaluate your deeply-rooted beliefs.

Before you go on with these 'real applications' of yours, may I ask what is your definition of infinity?

Are you speaking of potential infinity or actual infinity?
The thing is, I hate relativism. I hate relativism more than I hate everything else, excepting, maybe, fibreglass powerboats... What it overlooks, to put it briefly and crudely, is the fixed structure of human nature. - Jerry Fodor

Don't be a stat cynic:
http://www.debate.org...

Response to conservative views on deforestation:
http://www.debate.org...

Topics I'd like to debate (not debating ATM): http://tinyurl.com...
Dirty.Harry
Posts: 1,585
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2/7/2016 5:04:14 PM
Posted: 10 months ago
At 2/7/2016 4:31:54 PM, TREssspa wrote:
At 2/7/2016 4:15:53 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 3:58:37 PM, TREssspa wrote:
At 2/7/2016 2:35:22 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 1:11:13 PM, TREssspa wrote:
Is infinity used anywhere in mathematics?
I've given you a list once, and I'll give it to you again.
-Domains and ranges of certain functions
-Defining asymptotes
-Infinite series
-Improper integrals
-By extension, defining probability density functions of continuous random variables
-The cardinality of the set of natural numbers, etc.

The list goes on.
Does it exist in reality?
Or. .. is it just imagination?
Infinity doesn't exist in reality in the sense that you can't find an infinite number of anything. This doesn't disprove its theoretical importance in mathematics.

'No one shall expel us from the Paradise that Cantor has created.' - David Hilbert
Can anyone here prove (or disprove) infinity?

any real application?
Yeah, it might be more interesting to find a technical field that does not use calculus (which is, in a way, based on infinity) of any kind.

If you haven't noticed, I've already pointed out a 'real application': probability density functions, which make use of improper integrals. PDFs are important in statistics, which in turn is important in economics, actuarial sciences and other applications.

If you need more, calculus is important in calculating areas, volumes, velocities, lengths, and a variety of things that are essential in engineering applications.

I'm not sure if you'll believe me though: judging by your history on this site, you don't seem to be willing to re-evaluate your deeply-rooted beliefs.

Before you go on with these 'real applications' of yours, may I ask what is your definition of infinity?

There are numbers called irrational numbers, these are infinite sequences of digits - examples are the square root of two, there are also transcendental numbers like pi or e, these too are infinite sequences of digits.

If square root of two had a finite number of decimal places then it would be equal to a fraction the ratio of two integers.

The proof that root two is irrational is quite simple and is proof by contradiction:

http://www.math.utah.edu...

Harry.
Mhykiel
Posts: 5,987
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2/7/2016 7:46:30 PM
Posted: 10 months ago
At 2/7/2016 1:11:13 PM, TREssspa wrote:
Is infinity used anywhere in mathematics?

Yes the number line is an infinite continuum. A deductive argument of it's use in mathematics is easy. Think of any arbitrary large number and then add one. This can be done over and over again ad naseum to infinity.

Does it exist in reality?

You will have to elaborate on what you consider to be reality.

Or. .. is it just imagination?

numbers are abstract concepts that exist in the mind. Does that make them imaginary and un-useful to living in reality?


Can anyone here prove (or disprove) infinity?

The deductive argument earlier is a fair start.
keithprosser
Posts: 2,062
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2/7/2016 11:32:32 PM
Posted: 10 months ago
I'd guess there are no 'physical infinities' - that is nothing in real world is truly infinite.

On the other hand mathematical objects inhabit the 'mathematical realm', not the real world. Infinite mathematical objects certainly exist in that realm.... but in that realm only.
TREssspa
Posts: 567
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2/8/2016 8:31:26 AM
Posted: 10 months ago
At 2/7/2016 4:38:32 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 4:31:54 PM, TREssspa wrote:
At 2/7/2016 4:15:53 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 3:58:37 PM, TREssspa wrote:
At 2/7/2016 2:35:22 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 1:11:13 PM, TREssspa wrote:
Is infinity used anywhere in mathematics?
I've given you a list once, and I'll give it to you again.
-Domains and ranges of certain functions
-Defining asymptotes
-Infinite series
-Improper integrals
-By extension, defining probability density functions of continuous random variables
-The cardinality of the set of natural numbers, etc.

The list goes on.
Does it exist in reality?
Or. .. is it just imagination?
Infinity doesn't exist in reality in the sense that you can't find an infinite number of anything. This doesn't disprove its theoretical importance in mathematics.

'No one shall expel us from the Paradise that Cantor has created.' - David Hilbert
Can anyone here prove (or disprove) infinity?

any real application?
Yeah, it might be more interesting to find a technical field that does not use calculus (which is, in a way, based on infinity) of any kind.

If you haven't noticed, I've already pointed out a 'real application': probability density functions, which make use of improper integrals. PDFs are important in statistics, which in turn is important in economics, actuarial sciences and other applications.

If you need more, calculus is important in calculating areas, volumes, velocities, lengths, and a variety of things that are essential in engineering applications.

I'm not sure if you'll believe me though: judging by your history on this site, you don't seem to be willing to re-evaluate your deeply-rooted beliefs.

Before you go on with these 'real applications' of yours, may I ask what is your definition of infinity?

Are you speaking of potential infinity or actual infinity?

____________________
actual infinity.
Diqiucun_Cunmin
Posts: 2,710
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2/8/2016 8:55:56 AM
Posted: 10 months ago
At 2/8/2016 8:31:26 AM, TREssspa wrote:
At 2/7/2016 4:38:32 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 4:31:54 PM, TREssspa wrote:
At 2/7/2016 4:15:53 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 3:58:37 PM, TREssspa wrote:
At 2/7/2016 2:35:22 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 1:11:13 PM, TREssspa wrote:
Is infinity used anywhere in mathematics?
I've given you a list once, and I'll give it to you again.
-Domains and ranges of certain functions
-Defining asymptotes
-Infinite series
-Improper integrals
-By extension, defining probability density functions of continuous random variables
-The cardinality of the set of natural numbers, etc.

The list goes on.
Does it exist in reality?
Or. .. is it just imagination?
Infinity doesn't exist in reality in the sense that you can't find an infinite number of anything. This doesn't disprove its theoretical importance in mathematics.

'No one shall expel us from the Paradise that Cantor has created.' - David Hilbert
Can anyone here prove (or disprove) infinity?

any real application?
Yeah, it might be more interesting to find a technical field that does not use calculus (which is, in a way, based on infinity) of any kind.

If you haven't noticed, I've already pointed out a 'real application': probability density functions, which make use of improper integrals. PDFs are important in statistics, which in turn is important in economics, actuarial sciences and other applications.

If you need more, calculus is important in calculating areas, volumes, velocities, lengths, and a variety of things that are essential in engineering applications.

I'm not sure if you'll believe me though: judging by your history on this site, you don't seem to be willing to re-evaluate your deeply-rooted beliefs.

Before you go on with these 'real applications' of yours, may I ask what is your definition of infinity?

Are you speaking of potential infinity or actual infinity?

____________________
actual infinity.

http://mathworld.wolfram.com...
The thing is, I hate relativism. I hate relativism more than I hate everything else, excepting, maybe, fibreglass powerboats... What it overlooks, to put it briefly and crudely, is the fixed structure of human nature. - Jerry Fodor

Don't be a stat cynic:
http://www.debate.org...

Response to conservative views on deforestation:
http://www.debate.org...

Topics I'd like to debate (not debating ATM): http://tinyurl.com...
Diqiucun_Cunmin
Posts: 2,710
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2/8/2016 11:46:30 AM
Posted: 10 months ago
At 2/8/2016 8:55:56 AM, Diqiucun_Cunmin wrote:
At 2/8/2016 8:31:26 AM, TREssspa wrote:
At 2/7/2016 4:38:32 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 4:31:54 PM, TREssspa wrote:
At 2/7/2016 4:15:53 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 3:58:37 PM, TREssspa wrote:
At 2/7/2016 2:35:22 PM, Diqiucun_Cunmin wrote:
At 2/7/2016 1:11:13 PM, TREssspa wrote:
Is infinity used anywhere in mathematics?
I've given you a list once, and I'll give it to you again.
-Domains and ranges of certain functions
-Defining asymptotes
-Infinite series
-Improper integrals
-By extension, defining probability density functions of continuous random variables
-The cardinality of the set of natural numbers, etc.

The list goes on.
Does it exist in reality?
Or. .. is it just imagination?
Infinity doesn't exist in reality in the sense that you can't find an infinite number of anything. This doesn't disprove its theoretical importance in mathematics.

'No one shall expel us from the Paradise that Cantor has created.' - David Hilbert
Can anyone here prove (or disprove) infinity?

any real application?
Yeah, it might be more interesting to find a technical field that does not use calculus (which is, in a way, based on infinity) of any kind.

If you haven't noticed, I've already pointed out a 'real application': probability density functions, which make use of improper integrals. PDFs are important in statistics, which in turn is important in economics, actuarial sciences and other applications.

If you need more, calculus is important in calculating areas, volumes, velocities, lengths, and a variety of things that are essential in engineering applications.

I'm not sure if you'll believe me though: judging by your history on this site, you don't seem to be willing to re-evaluate your deeply-rooted beliefs.

Before you go on with these 'real applications' of yours, may I ask what is your definition of infinity?

Are you speaking of potential infinity or actual infinity?

____________________
actual infinity.

http://mathworld.wolfram.com...

I will add that most of the applications use potential infinity though.
The thing is, I hate relativism. I hate relativism more than I hate everything else, excepting, maybe, fibreglass powerboats... What it overlooks, to put it briefly and crudely, is the fixed structure of human nature. - Jerry Fodor

Don't be a stat cynic:
http://www.debate.org...

Response to conservative views on deforestation:
http://www.debate.org...

Topics I'd like to debate (not debating ATM): http://tinyurl.com...
RuvDraba
Posts: 6,033
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2/10/2016 11:08:08 AM
Posted: 10 months ago
At 2/7/2016 1:11:13 PM, TREssspa wrote:
Is infinity used anywhere in mathematics?
Yes, transfinite numbers [https://en.wikipedia.org...] can be used in set theory [http://www.math.utah.edu...]

Does it exist in reality?
I think we'd need to agree on definitions of 'exist' and 'reality' before we answered that, TRE.

But science validates its ideas based on empiricism -- information supplied by sensory observation. Our observations being finite in number, and our senses providing only finite information in each observation, there may be no way to 'observe' the infinite -- only to model it. And if we define reality as only what we can verify through observation, then an unobservable infinity may be invalid when described as anything but an imaginary ideal.

Moreover it may not be clear how to falsify the existence of infinite quantities. And unfalsifiable ideas can also be treated as invalid in science.

Lastly, there are practical reasons to avoid performing logic directly with infinite quantities. Unless one is careful, there's the risk of assuming things one might not be actually able to do (like choosing an element from an infinite number of elements, or uniquely identifying what element one has chosen.) In certain cases, infinite regress can also lead to unsoundness -- that is, the ability to prove both a proposition and its contradiction, which destroys a key property we normally want from logic.

But with all that said, scientific modeling often treats certain ideas as infinite -- time and space are often treated as a continuum, for example, such that between any two points there are more points, and so many points that there are no 'gaps' between them.

The proposition that time and space are infinitely dense is an hypothesis, and to the best of my knowledge it has neither been proven nor disproven, either logically or physically. So it's often treated as true until falsified -- perhaps because it's not clear how, why or when to treat it as false. :D

I hope that may help, TRE. Links available on specific request.