A Genuine Question In Mathematical Philosophy

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A Genuine Question In Mathematical Philosophy
I offer the following question.
(1) Mainstream mathematics assures us there are several proofs to show that 0.999... = 1.
(2) Peano Arithmetic and Set Theory (as conjoined and exemplified, for example, in Cantor's Diagonal Argument) tell us that 0.999... is the largest real number which is less than 1.
(3) If 0.999... = 1, it would appear that parallel lines, and lines which intersect at infinity, are mathematically indistinguishable, with significant consequences for Euclidean geometry.
May I solicit your comments?
(1) Mainstream mathematics assures us there are several proofs to show that 0.999... = 1.
(2) Peano Arithmetic and Set Theory (as conjoined and exemplified, for example, in Cantor's Diagonal Argument) tell us that 0.999... is the largest real number which is less than 1.
(3) If 0.999... = 1, it would appear that parallel lines, and lines which intersect at infinity, are mathematically indistinguishable, with significant consequences for Euclidean geometry.
May I solicit your comments?

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Re: A Genuine Question In Mathematical Philosophy
This has been reported. Keep your personal problems... personal!Alan Masterman wrote: ↑February 15th, 2018, 7:31 amOn the offchance that this is still a serious philosophy forum, and hasn't been totally hijacked by Growthhormone and those silly enough to dignify his or her posts with a reply, I offer the following question.
Violation the ToS.
Is absurd!0.999... = 1.
Ultimately, it is no more than a desperate attempt by 'believers' to justify the obsolete belief in materialism/physicalism. It is meaningless, emotional, crap.
That also means that the notion/definition of a tangent must be dismissed as an impossibility.
It is pathetic.

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Re: A Genuine Question In Mathematical Philosophy
.999 approaches 1 as you add nines

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Re: A Genuine Question In Mathematical Philosophy
I think I may have replied to Growthhormone, but fortunately my posts aren't capable of dignifying anything.Alan Masterman wrote:...those silly enough to dignify his or her posts with a reply
I assume you mean an infinite number of 9's. I would have thought that mathematics says something more like "0.999... tends towards 1 as the number of 9's increases", which is a different thing. By increasing the number of 9's you can get arbitrarily close to 1, which means that for any given number of 9's it's always possible to add another.Alan Masterman wrote:Mainstream mathematics assures us there are several proofs to show that 0.999... = 1.
I've never known anybody to get angry about sums before. Great stuff.Namelesss wrote:Ultimately, it is no more than a desperate attempt by 'believers' to justify the obsolete belief in materialism/physicalism. It is meaningless, emotional, crap...
Yes. Sounds reasonable.Chili wrote:.999 approaches 1 as you add nines
"When the seagulls follow the trawler, it is because they think sardines will be thrown into the sea."  Eric Cantona.

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Re: A Genuine Question In Mathematical Philosophy
Glad you can appreciate it. *__
The emotion is because people identifying with their beliefs; materialism, in this case.
When a 'belief' feels threatened, so does the person.
That is why emotion, at some level, rather than rational/logical thought becomes involved...
Or, you've never seen, or been, someone working hard at the old blackboard and, at some point, feels frustration? Frustration is the feeling, anger the expression (or one expression).
(Throws chalk across room over sums!)

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Re: A Genuine Question In Mathematical Philosophy
OK. But I would hope you're at least aware of the absurdity of saying that the statement:
"0.999... = 1"
is
"no more than a desperate attempt by 'believers' to justify the obsolete belief in materialism/physicalism. It is meaningless, emotional, crap."
It's just somebody making a proposition about the nature of infinitesimals and limits.
"0.999... = 1"
is
"no more than a desperate attempt by 'believers' to justify the obsolete belief in materialism/physicalism. It is meaningless, emotional, crap."
It's just somebody making a proposition about the nature of infinitesimals and limits.
"When the seagulls follow the trawler, it is because they think sardines will be thrown into the sea."  Eric Cantona.

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Re: A Genuine Question In Mathematical Philosophy
And now we have two Perspectives.Steve3007 wrote: ↑February 20th, 2018, 8:25 amOK. But I would hope you're at least aware of the absurdity of saying that the statement:
"0.999... = 1"
is
"no more than a desperate attempt by 'believers' to justify the obsolete belief in materialism/physicalism. It is meaningless, emotional, crap."
It's just somebody making a proposition about the nature of infinitesimals and limits.
Go play with someone else.

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Re: A Genuine Question In Mathematical Philosophy
To Alan Masterman:
If you treat others with a little respect, and don't simply dismiss them with expletives, you may get some respect in return. If you don't, you probably won't. If a subject as innocuous as mathematics causes an emotional reaction in you, then, as you yourself have said to the original poster in this topic, this is your personal problem. Perhaps you should keep it to yourself?
Namelesss, can you see the irony/hypocrisy in your saying this, given that so many of your own posts contain derisory, ad hominem, snarky or sarcastic comments against the people who are trying to talk with you?Namelesss wrote:This has been reported. Keep your personal problems... personal!
Violation the ToS.
Namelesss wrote:It is meaningless, emotional, crap.
(STFU is an acronym for "Shut the f**k up".)Namelesss wrote:Then feel free to STFU and listen.
etc.Namelesss wrote:Go play with someone else.
If you treat others with a little respect, and don't simply dismiss them with expletives, you may get some respect in return. If you don't, you probably won't. If a subject as innocuous as mathematics causes an emotional reaction in you, then, as you yourself have said to the original poster in this topic, this is your personal problem. Perhaps you should keep it to yourself?
"When the seagulls follow the trawler, it is because they think sardines will be thrown into the sea."  Eric Cantona.
 mathman
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Re: A Genuine Question In Mathematical Philosophy
I think what he meant was 0.999 APPROACHES 1. 0.9999 would be larger to 1 than the former. So keep adding 9's would not reach "1" ever because the number would in fact become smaller each time required to get to "1" but it tends to 1 in the mathematical sense as the first significant figure after the decimal ruled it out of ever becoming a "1".

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Re: A Genuine Question In Mathematical Philosophy
One way to express it is to use the language of the Theory of Limits and say that 1 is the limiting value of 0.999 as the number of decimal places tends towards infinity. This is different from simply saying "0.999... = 1".
http://people.sju.edu/~pklingsb/limitthy.pdf
http://people.sju.edu/~pklingsb/limitthy.pdf
"When the seagulls follow the trawler, it is because they think sardines will be thrown into the sea."  Eric Cantona.
 Atreyu
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Re: A Genuine Question In Mathematical Philosophy
I remember than in my high school geometry class our teacher taught us that .9999.... = 1
One way he proved it was by multiplying each side of the equation '.3333...= 1/3' by 3.
Right?
One way he proved it was by multiplying each side of the equation '.3333...= 1/3' by 3.
Right?

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Re: A Genuine Question In Mathematical Philosophy
I am glad you are asking about mathematical philosophy rather than mathematics. In mathematical philosophy, the philosophical concept of infinity can exist. Infinity does not exist in mathematics because it is purely conceptual and has no value. This is similar to eternity not being a unit of time.
Unfortunately, modern physics since the turn of the century has mistakenly confused infinity as a mathematical quantity. Einstein’s general theory of relativity is derived from this type of mathemagics. Steven Hawking would speak of “near infinite temperatures” when explaining the Big Bang. So, how close to infinity does one have to get to be “near” it? Would this be infinity minus 100, 1,000, 1 billion degrees? Just plain silly in my opinion.
Most theoretical math in physics these days is mathematical philosophy rather than mathematics. Mathematics is for making testable predictions, not for philosophizing about black holes that nobody can create experiments around (and no BoseEinstein condensates, please). Black holes fall within the discipline of mathemagics. It’s how clever physicists or theoretical mathematicians fool the general public and “find” Higgs Bosons for a mere $15B!
So, according to mathematical philosophy, or metaphysics, YES, your infinite 0.9999... equals exactly one. However, I would not try to cheat the stock market with such mathematical trickery.
Cheers
Unfortunately, modern physics since the turn of the century has mistakenly confused infinity as a mathematical quantity. Einstein’s general theory of relativity is derived from this type of mathemagics. Steven Hawking would speak of “near infinite temperatures” when explaining the Big Bang. So, how close to infinity does one have to get to be “near” it? Would this be infinity minus 100, 1,000, 1 billion degrees? Just plain silly in my opinion.
Most theoretical math in physics these days is mathematical philosophy rather than mathematics. Mathematics is for making testable predictions, not for philosophizing about black holes that nobody can create experiments around (and no BoseEinstein condensates, please). Black holes fall within the discipline of mathemagics. It’s how clever physicists or theoretical mathematicians fool the general public and “find” Higgs Bosons for a mere $15B!
So, according to mathematical philosophy, or metaphysics, YES, your infinite 0.9999... equals exactly one. However, I would not try to cheat the stock market with such mathematical trickery.
Cheers
 Jacqueline Sheehan
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Re: A Genuine Question In Mathematical Philosophy
https://en.wikipedia.org/wiki/0.999...
There are many ways to prove that 0.999... = 1,
Infinite series, algebra arguments, etc.
There are many ways to prove that 0.999... = 1,
Infinite series, algebra arguments, etc.
 Halc
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Re: A Genuine Question In Mathematical Philosophy
Unclear how genuine your interest is in any of this. You've not posted a single response since opening this topic.Alan Masterman wrote: ↑February 15th, 2018, 7:31 am(1) Mainstream mathematics assures us there are several proofs to show that 0.999... = 1.
From what I've read by those that are more experts in this subject than I, this issue was unresolved for some time, and certain fundamental axioms had to be assumed for them to say these were equal. If different axioms are assumed, they are not equal. But mainstream mathematics runs under the former axioms. The other axioms are not wrong because of this. They're just not as mainstream.
This seems contradictory, but maybe I'm wrong. This seems to imply that .999... is unequal to 1, but the average between these two unequal numbers does not lie between them, or if it does, then .999... is not the largest real number less than 1. How is that not a contradiction?(2) Peano Arithmetic and Set Theory (as conjoined and exemplified, for example, in Cantor's Diagonal Argument) tell us that 0.999... is the largest real number which is less than 1.
What would these consequences be? Indistinguishable doesn't mean there is actually a point of intersection since infinity isn't a specific number, else they'd cross there and grow apart at points beyond infinity.(3) If 0.999... = 1, it would appear that parallel lines, and lines which intersect at infinity, are mathematically indistinguishable, with significant consequences for Euclidean geometry.
A few random comments:
True, but .999... is not the same as a series with a limit. It is a number with no more 9's to 'keep adding', and numbers don't approach anything.
This is begging and thus an invalid proof. If 0.999... is not equal to 1, then 0.333... is not equal to 1/3. So one must assume the conclusion to prove the conclusion.