A Genuine Question In Mathematical Philosophy
 hanahana
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Re: A Genuine Question In Mathematical Philosophy
this is a very useful post...well done
Graduated from Soran University with First Class Degree with Honours in Computer Science
Graduated from Soran University with First Class Degree with Honours in Computer Science
 Steve3007
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 Joined: June 15th, 2011, 5:53 pm
 Favorite Philosopher: Eratosthenes of Cyrene
 Location: UK
Re: A Genuine Question In Mathematical Philosophy
There's an interesting sum of a geometrical series in the song "Take It Easy" by The Eagles. It goes like this:
"I'm running down the road trying to loosen my load,
I got 7 women on my mind,
4 that want to own me,
2 that want to stone me,
1 says she's a friend of mine.
Take it easy. Take is easy.
Don't let the sound of your own wheels drive you crazy."
But the trouble is, The Eagles didn't finish this geometrical progression (in which each number is 0.5 times the previous one). If they had finished it to infinity, would the total number of women on the songwriter's mind by 8, not 7? And would it be acceptable, after the first 3 terms, for him to have an infinite number of women's body parts on his mind?
"I'm running down the road trying to loosen my load,
I got 7 women on my mind,
4 that want to own me,
2 that want to stone me,
1 says she's a friend of mine.
Take it easy. Take is easy.
Don't let the sound of your own wheels drive you crazy."
But the trouble is, The Eagles didn't finish this geometrical progression (in which each number is 0.5 times the previous one). If they had finished it to infinity, would the total number of women on the songwriter's mind by 8, not 7? And would it be acceptable, after the first 3 terms, for him to have an infinite number of women's body parts on his mind?

 Posts: 1347
 Joined: April 19th, 2016, 2:53 pm
Re: A Genuine Question In Mathematical Philosophy
And could he imagine what a half of a hydrogen atom looks like?Steve3007 wrote: ↑December 10th, 2018, 6:53 am There's an interesting sum of a geometrical series in the song "Take It Easy" by The Eagles. It goes like this:
"I'm running down the road trying to loosen my load,
I got 7 women on my mind,
4 that want to own me,
2 that want to stone me,
1 says she's a friend of mine.
Take it easy. Take is easy.
Don't let the sound of your own wheels drive you crazy."
But the trouble is, The Eagles didn't finish this geometrical progression (in which each number is 0.5 times the previous one). If they had finished it to infinity, would the total number of women on the songwriter's mind by 8, not 7? And would it be acceptable, after the first 3 terms, for him to have an infinite number of women's body parts on his mind?

 Posts: 70
 Joined: March 27th, 2011, 8:03 am
Re: A Genuine Question In Mathematical Philosophy
Thank you everybody for the privilege of your attention. I deliberately refrained from joining the discussion because I wanted to see how it would develop without my input. But mainly, because I lost the thread and took this long to find it again.
The balance of responses, by and large, appear to support my thesis that the science of mathematics is NOT the monolithic, logicallyperfect entity that the layperson tends to assume it is. There are many mutuallyinconsistent areas. I thank especially Steve3007, Nameless, Mathman, and Halc for their inputs.
The balance of responses, by and large, appear to support my thesis that the science of mathematics is NOT the monolithic, logicallyperfect entity that the layperson tends to assume it is. There are many mutuallyinconsistent areas. I thank especially Steve3007, Nameless, Mathman, and Halc for their inputs.
 Felix
 Posts: 3117
 Joined: February 9th, 2009, 5:45 am
Re: A Genuine Question In Mathematical Philosophy
Steve3007: "If they had finished it to infinity..."
That would be contrary to the song's advice: "Take it easy. Take it easy. Don't let the sound of your own wheels drive you crazy."
Happens all the time here, i.e., the sound of people's own cognitive wheels driving them crazy.
That would be contrary to the song's advice: "Take it easy. Take it easy. Don't let the sound of your own wheels drive you crazy."
Happens all the time here, i.e., the sound of people's own cognitive wheels driving them crazy.
"We do not see things as they are; we see things as we are."  Anaïs Nin

 Posts: 70
 Joined: March 27th, 2011, 8:03 am
Re: A Genuine Question In Mathematical Philosophy
Philosophically speaking, the fundamental question is: what is the smallest possible number? One can represent it various ways, eg:
h
0.0...1
1/(whatever symbol for infinity can be copied accurately to this message box)
The Planck Number
h
0.0...1
1/(whatever symbol for infinity can be copied accurately to this message box)
The Planck Number

 Posts: 51
 Joined: July 19th, 2016, 11:25 am
 Location: Koenigsberg (7 bridges problem)
Re: A Genuine Question In Mathematical Philosophy
Hi Alan Masterman,
Are you asking about the smallest positive real number? Just want to clarify it for myself before to continue.
And by the way what makes you sure that 1/infinity is a real number?
Thanks.
Are you asking about the smallest positive real number? Just want to clarify it for myself before to continue.
And by the way what makes you sure that 1/infinity is a real number?
Thanks.
 detail
 Posts: 138
 Joined: June 1st, 2019, 1:39 pm
Re: A Genuine Question In Mathematical Philosophy
The problem is that easy is not measurable in numbers, thats why he didn't finish via total induction.Tamminen wrote: ↑December 10th, 2018, 8:45 amAnd could he imagine what a half of a hydrogen atom looks like?Steve3007 wrote: ↑December 10th, 2018, 6:53 am There's an interesting sum of a geometrical series in the song "Take It Easy" by The Eagles. It goes like this:
"I'm running down the road trying to loosen my load,
I got 7 women on my mind,
4 that want to own me,
2 that want to stone me,
1 says she's a friend of mine.
Take it easy. Take is easy.
Don't let the sound of your own wheels drive you crazy."
But the trouble is, The Eagles didn't finish this geometrical progression (in which each number is 0.5 times the previous one). If they had finished it to infinity, would the total number of women on the songwriter's mind by 8, not 7? And would it be acceptable, after the first 3 terms, for him to have an infinite number of women's body parts on his mind?

 Posts: 70
 Joined: March 27th, 2011, 8:03 am
Re: A Genuine Question In Mathematical Philosophy
I guess this thread is just about played out, so I will make a final comment. Thank you, everybody, for your comments.
Firstly, the question whether 0.999...=1 is mathematically profoundly important. Why does it matter to Euclidean geometry? Because for more than 2,500 years, the problem of the Parallel Postulate has been a thorn in the side of mathematical philosophers. In the Elements, Euclid nowhere dares to state a parallel postulate explicitly, because there is no LOGICALLY compelling reason to suppose that any such thing exists. That's why it's only an axiom ("assertion without proof"), not a theorem. But if 0.999 ...=1, the problem is solved, because the concept of parallel lines (as traditionally understood) becomes irrelevant to Euclidean geometry. Thus the problematic Euclidean concept of "parallel lines" can be dispensed with. You don't think this is a big deal?
Again, if 0.999...=1, then Cantor's diagonal argument  which underpins theories of infinity, without which modern mathematics doesn't work  collapses in a heap. In fact, taken to its logical conclusion, every real number between 0 and 1 will equal both 0 and 1. No big deal?
Like some of the respondents, I do not accept the supposed proof from limit theory. There is a difference between a proof, and a mere demonstration of noncontradiction. The challenge for those who maintain that 0.999...=1 as a universal truth  and there ARE those who do so vociferously  is, to prove that this theorem is necessarily true for all of mathematics, not merely contingently true for limit theory (assuming they understand the difference between necessity and contingency, which I think not many mathematicians appreciate fully); and to explain what modifications to the axioms of arithmetic would be needed to remove the contradictions this would generate.
Firstly, the question whether 0.999...=1 is mathematically profoundly important. Why does it matter to Euclidean geometry? Because for more than 2,500 years, the problem of the Parallel Postulate has been a thorn in the side of mathematical philosophers. In the Elements, Euclid nowhere dares to state a parallel postulate explicitly, because there is no LOGICALLY compelling reason to suppose that any such thing exists. That's why it's only an axiom ("assertion without proof"), not a theorem. But if 0.999 ...=1, the problem is solved, because the concept of parallel lines (as traditionally understood) becomes irrelevant to Euclidean geometry. Thus the problematic Euclidean concept of "parallel lines" can be dispensed with. You don't think this is a big deal?
Again, if 0.999...=1, then Cantor's diagonal argument  which underpins theories of infinity, without which modern mathematics doesn't work  collapses in a heap. In fact, taken to its logical conclusion, every real number between 0 and 1 will equal both 0 and 1. No big deal?
Like some of the respondents, I do not accept the supposed proof from limit theory. There is a difference between a proof, and a mere demonstration of noncontradiction. The challenge for those who maintain that 0.999...=1 as a universal truth  and there ARE those who do so vociferously  is, to prove that this theorem is necessarily true for all of mathematics, not merely contingently true for limit theory (assuming they understand the difference between necessity and contingency, which I think not many mathematicians appreciate fully); and to explain what modifications to the axioms of arithmetic would be needed to remove the contradictions this would generate.

 Posts: 70
 Joined: March 27th, 2011, 8:03 am
Re: A Genuine Question In Mathematical Philosophy
wow, this whole thread is better than an acid trip!
"Unclear how genuine your interest is in any of this. You've not posted a single response since opening this topic."
Troll warning: this is a personal attack on the contributor, and any repetition may result in a formal complaint being lodged against you with the moderators.
Here and there, one or two contributors made intelligent comments, for which I thank you. You know who you are.
"Unclear how genuine your interest is in any of this. You've not posted a single response since opening this topic."
Troll warning: this is a personal attack on the contributor, and any repetition may result in a formal complaint being lodged against you with the moderators.
Here and there, one or two contributors made intelligent comments, for which I thank you. You know who you are.