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Bones McCracker Veteran
Joined: 14 Mar 2006 Posts: 1577 Location: U.S.A.

Posted: Thu Jun 20, 2013 6:29 pm Post subject: The rise of radical, militant... Buddhism 


Quote:  After a ritual prayer atoning for past sins, Ashin Wirathu, a Buddhist monk with a rockstar following in Myanmar, sat before an overflowing crowd of thousands of followers and launched into a rant against what he called the “enemy” — the country’s Muslim minority. Ashin Wirathu denies any role in riots in which Buddhist mobs have killed more than 200 Muslims and forced more than 150,000 people, from their homes. mostly Muslims, 
http://www.nytimes.com/slideshow/2013/06/20/world/asia/20130620_BUDDHIST.html _________________ Behold the tortoise: he only makes progress when he sticks out his neck. Behold the vampire bat: he really sucks. 

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dmitchell Veteran
Joined: 17 May 2003 Posts: 1159 Location: Austin, Texas

Posted: Thu Jun 20, 2013 6:37 pm Post subject: 


Militant Buddhism? I feel like somebody just divided by zero in my head. _________________ Your argument is invalid. 

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LoTeK Apprentice
Joined: 26 Jul 2012 Posts: 270

Posted: Thu Jun 20, 2013 7:18 pm Post subject: 


It's a common misunderstanding that buddhists are only peaceful, but nevertheless the most likable religion (btw maybe the only atheistic religion ).
I always asked myself why we "can not divide by zero". I mean since most people think that numbers are only "fictive" or a "pure invention of the human mind", why shouldn't we be able to invent a mathematical theory with a consistent definition of the division by zero?
on the other hand those old fashion platonists like me that think the mathematical reality is real and even more real than the physical world, why does division by zero leads to contradictions? what does it even mean?
edit: anyone here that knows dante 01? a french science fiction movie with a psychopathic buddhist murderer that kills people to give them salvation _________________ "I want to see gamma rays! I want to hear Xrays! Do you see the absurdity of what I am? I can't even express these things properly because I have to conceptualize complex ideas in this stupid limiting spoken language!"
Last edited by LoTeK on Thu Jun 20, 2013 7:41 pm; edited 1 time in total 

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Bones McCracker Veteran
Joined: 14 Mar 2006 Posts: 1577 Location: U.S.A.

Posted: Thu Jun 20, 2013 7:36 pm Post subject: 


I used to love the show, Kung Fu, so I like the idea of a bunch of Buddhist monks kicking ass.
We need a Quentin Tarantino movie about this. _________________ Behold the tortoise: he only makes progress when he sticks out his neck. Behold the vampire bat: he really sucks. 

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BonezTheGoon Bodhisattva
Joined: 14 Jun 2002 Posts: 1375 Location: Albuquerque, NM  birthplace of Microsoft and Gentoo

Posted: Thu Jun 20, 2013 8:55 pm Post subject: 


LoTeK wrote:  . . . (btw maybe the only atheistic religion ) . . . 
http://en.wikipedia.org/wiki/Atheism wrote:  Atheism is accepted within some religious and spiritual belief systems, including Hinduism, Jainism, Buddhism, Raelism, Neopagan movements[19] such as Wicca,[20] and nontheistic religions. Jainism and some forms of Buddhism do not advocate belief in gods,[21] whereas Hinduism holds atheism to be valid, but some schools view the path of an atheist to be difficult to follow in matters of spirituality.[22] 
_________________
pjp wrote:  The greater evil is voting for the "lesser evil." 


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BonezTheGoon Bodhisattva
Joined: 14 Jun 2002 Posts: 1375 Location: Albuquerque, NM  birthplace of Microsoft and Gentoo

Posted: Thu Jun 20, 2013 9:00 pm Post subject: 


LoTeK wrote:  . . . what does it even mean? . . . 
What does divide by zero mean? Well it is instructions to divide up some thing into oblivion, into zero pieces. So division by zero is a impossibility, because you cannot divide or section something into nothing.
It would be like me telling you to cut a pie into zero pieces. It is physically impossible to cut a pie into zero pieces. You can cut it into any positive number of pieces, including one piece which is to say that it remains uncut. _________________
pjp wrote:  The greater evil is voting for the "lesser evil." 


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Bigun Veteran
Joined: 21 Sep 2003 Posts: 1974

Posted: Thu Jun 20, 2013 9:39 pm Post subject: 


BonezTheGoon wrote:  LoTeK wrote:  . . . what does it even mean? . . . 
What does divide by zero mean? Well it is instructions to divide up some thing into oblivion, into zero pieces. So division by zero is a impossibility, because you cannot divide or section something into nothing.
It would be like me telling you to cut a pie into zero pieces. It is physically impossible to cut a pie into zero pieces. You can cut it into any positive number of pieces, including one piece which is to say that it remains uncut. 
It's a coding issue programmers have to account for. In my career of coding, I've ran into it a total of one (1) time, and had to debug it.
Take any number, divide by zero, and you get an error. You can even demonstrate it on most calculators. 

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aCOSwt Moderator
Joined: 19 Oct 2007 Posts: 2537 Location: Hilbert space

Posted: Thu Jun 20, 2013 10:40 pm Post subject: 


LoTeK wrote:  I always asked myself why we "can not divide by zero"...why shouldn't we be able to invent a mathematical theory with a consistent definition of the division by zero? 
Done! && interesting indeed.
No need for any new or particular theory : Contrarily to what the other contributors said, dividing by 0 is absolutely neither illegal nor meaningless in maths.
In maths, the fact that some operation is legal or not depends on the set you are working on.
For example, if you are working on ℝ (Real numbers) extracting the square root of a negative number is absolutely illegal.
But, the square root of a negative number is perfectly legal if you are working on ℂ (complex numbers)
The same goes with the division by 0.
Of course it is perfectly illegal if you are working on ℝ.
Why is it illegal ? Not because of the fancy reasons given by Bigun & BonezTheGoon.
It is illegal because ℝ is defined on ]∞;+∞[
You notice that ∞ (infinity) does not belong to the set and as ∞ would be the result of a division by 0, if the result does not belong to the set, then the operation is not permitted. Period!
So... we now understand that, in order to make a division by 0 perfectly legal and usable, we just need to work on a set in which infinity is included.
something like ℝ ⋃ {∞} would perfectly fit. If I state working on such a set, then, dividing by 0 is indeed perfectly and legal and defined and meaningful.
Interesting ? Important ? Valuable ? Significantly used ? Well... ℂ ⋃ {∞} almost certainly. It's called the Riemann sphere _________________


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GabrielYYZ n00b
Joined: 03 May 2012 Posts: 18 Location: Dominican Republic

Posted: Thu Jun 20, 2013 11:05 pm Post subject: 


BoneKracker wrote:  I used to love the show, Kung Fu, so I like the idea of a bunch of Buddhist monks kicking ass.
We need a Quentin Tarantino movie about this. 
"Baba Ram Django Unchained".
I'd watch it. 

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big dave n00b
Joined: 03 Jul 2009 Posts: 0 Location: land of first world problems

Posted: Thu Jun 20, 2013 11:20 pm Post subject: 


meeting a single tenet of atheism, the lack of belief in a god... sure.
but atheism is usually bound with science, and the science that also leads one to believe there is no god, usually also leads one to believe there is no satan and no reincarnation. 

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Bones McCracker Veteran
Joined: 14 Mar 2006 Posts: 1577 Location: U.S.A.

Posted: Fri Jun 21, 2013 12:00 am Post subject: 


Science also leads one to believe that time as we know it is an invalid concept (for example, effects can occur before the events that caused them). Science  our halfbaked understanding of reality  is not much use if one is looking for a rock of rationality upon which to cling. _________________ Behold the tortoise: he only makes progress when he sticks out his neck. Behold the vampire bat: he really sucks. 

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Darth Marley Tux's lil' helper
Joined: 25 Jan 2007 Posts: 105

Posted: Fri Jun 21, 2013 1:25 am Post subject: 


Just develop a base zero number system. When zero is 1, there is no error. 

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Prenj n00b
Joined: 20 Nov 2011 Posts: 16

Posted: Fri Jun 21, 2013 1:37 am Post subject: 


Too funny.
I wondered that exact same thing about buddhism, while it really sounds cool in theory, I am not sure that nonaggression is proper response when someone has clear intent of bashing you on the head. Not that it justifies preemptive strikes. But yeah, it just shows that there is no One True Way ever. 

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notageek Tux's lil' helper
Joined: 05 Jun 2008 Posts: 121 Location: U.S.A

Posted: Fri Jun 21, 2013 1:59 am Post subject: 


I'd watch a Kung Foo, Buddhist movie from Tarantino. _________________ 1958. It's been traveling twentytwo years to get here. And now it's here. And it's either heads or tails. And you have to say. Call it. 

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pjp Administrator
Joined: 16 Apr 2002 Posts: 16138 Location: Colorado

Posted: Fri Jun 21, 2013 2:15 am Post subject: 


The movie would be better if done by Rodriquez. Tarantino is a hack.
LoTeK wrote:  I always asked myself why we "can not divide by zero". I mean since most people think that numbers are only "fictive" or a "pure invention of the human mind", why shouldn't we be able to invent a mathematical theory with a consistent definition of the division by zero?  Because the Bible was written saying you cannot do it. _________________ lolgov. 'cause where we're going, you don't have civil liberties.
In Loving Memory
1787  2008 

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JohnBoy Guru
Joined: 23 Jun 2004 Posts: 439 Location: Desperately seeking moksha in all the wrong places

Posted: Fri Jun 21, 2013 5:54 am Post subject: 


dmitchell wrote:  Militant Buddhism? I feel like somebody just divided by zero in my head. 
Amazing religion Islam, you know you're in trouble with the pacifists start kicking off. _________________ Easy .. easy .. easy 

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sikpuppy n00b
Joined: 12 Jun 2012 Posts: 34 Location: Central Coast, NSW

Posted: Fri Jun 21, 2013 6:04 am Post subject: 


Yeah, I think nonviolence from Buddhism is about as shocking as bastard Catholics or alcoholic Muslims...in other words not very shocking at all. Also see evangelical television types and their various sins perpetrated in violation of their own verbal diarrhoea style preachings. 

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Muso l33t
Joined: 22 Oct 2002 Posts: 659 Location: The Holy city of Honolulu

Posted: Fri Jun 21, 2013 7:30 am Post subject: 


I was actually a couple hours shy of being killed by murderous bastards trying to cloak themselves with Buddhism. The day of the Om Shinrikyo attacks on the Tokyo metro lines, I was using both the Hibiya & Yamanote lines.
The difference between Om Shinrikyo and your run of the mill Islamists is this : Nowhere in Buddhism is there a call to violence. The Qur'an itself is a call to violence. _________________ "Giving money and power to government is like giving whiskey and car keys to teenage boys."  P. J. O'Rourke
There is no god but Bach, Beethoven is the messenger of Bach. 

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LoTeK Apprentice
Joined: 26 Jul 2012 Posts: 270

Posted: Fri Jun 21, 2013 5:03 pm Post subject: 


BonezTheGoon wrote:  LoTeK wrote:  . . . (btw maybe the only atheistic religion ) . . . 
http://en.wikipedia.org/wiki/Atheism wrote:  Atheism is accepted within some religious and spiritual belief systems, including Hinduism, Jainism, Buddhism, Raelism, Neopagan movements[19] such as Wicca,[20] and nontheistic religions. Jainism and some forms of Buddhism do not advocate belief in gods,[21] whereas Hinduism holds atheism to be valid, but some schools view the path of an atheist to be difficult to follow in matters of spirituality.[22] 

interesting.. but "normal" hinduism is full with many gods. I think buddhism is very different than christianity, judaism and islam while hinduism is closer to them.
Bigun wrote:  What does divide by zero mean? Well it is instructions to divide up some thing into oblivion, into zero pieces. So division by zero is a impossibility, because you cannot divide or section something into nothing.
It would be like me telling you to cut a pie into zero pieces. It is physically impossible to cut a pie into zero pieces. You can cut it into any positive number of pieces, including one piece which is to say that it remains uncut. 
if something is physically impossible or not is something very different from defining a mathematical operation. First you can argue that you can destroy the cake with an antimatter cake and say that you have divided it by zero Second and more important: it's absolutely unimportant if an operation or a concept is present in our known world. For example the game of chess is completely "unreal", but a chess player or a mathematician that tries to develop a winning strategy for the chess game couldn't care less if chess "happens in the real world".
Bigun wrote:  Take any number, divide by zero, and you get an error. You can even demonstrate it on most calculators. 
aCOSwt wrote: 
Done! && interesting indeed.
No need for any new or particular theory : Contrarily to what the other contributors said, dividing by 0 is absolutely neither illegal nor meaningless in maths.
In maths, the fact that some operation is legal or not depends on the set you are working on.
For example, if you are working on ℝ (Real numbers) extracting the square root of a negative number is absolutely illegal.
But, the square root of a negative number is perfectly legal if you are working on ℂ (complex numbers)
The same goes with the division by 0.
Of course it is perfectly illegal if you are working on ℝ.
Why is it illegal ? Not because of the fancy reasons given by Bigun & BonezTheGoon.
It is illegal because ℝ is defined on ]∞;+∞[
You notice that ∞ (infinity) does not belong to the set and as ∞ would be the result of a division by 0, if the result does not belong to the set, then the operation is not permitted. Period!
So... we now understand that, in order to make a division by 0 perfectly legal and usable, we just need to work on a set in which infinity is included.
something like ℝ ⋃ {∞} would perfectly fit. If I state working on such a set, then, dividing by 0 is indeed perfectly and legal and defined and meaningful.
Interesting ? Important ? Valuable ? Significantly used ? Well... ℂ ⋃ {∞} almost certainly. It's called the Riemann sphere

Thanks for the good answer, unfortunately you didn't say something I didn't know already (did you study math, computer science or physics?). since 0 is a finite element in ℝ it's strange that we need infinity for the division by zero, isn't it? I mean if you want to take square roots from negative numbers you can construct ℂ and maybe there were some "problems" with i, but since a "real number" is either as imaginary as an "imaginary number" or an "imaginary number" is as real as a "real number" depending on ones philosophical position (platonism vs formalism vs contructivism etc), therefore I don't see any problem with ℂ, but if you need infinity for a division operation it's weird (maybe I'm on the wrong way like those that didn't accepted ℂ )
big dave wrote:  but atheism is usually bound with science, and the science that also leads one to believe there is no god, usually also leads one to believe there is no satan and no reincarnation. 
again a common misunderstanding. many scientists were religious. maybe at the moment there is some kind of a trend to atheism, but that has nothing to do with science. especially many mathematicians were very religious (for example Gödel and cantor, he discussed the concept of infinity with catholic theologists). Or the very good quote from Heisenberg:
Quote:  "Der erste Schluck aus dem Becher der Wissenschaft führt zum Atheismus, aber auf dem Grund des Bechers wartet Gott.“ 
BoneKracker wrote:  Science also leads one to believe that time as we know it is an invalid concept (for example, effects can occur before the events that caused them). Science  our halfbaked understanding of reality  is not much use if one is looking for a rock of rationality upon which to cling. 
maybe because time as we know it is an invalid concept!? But I agree with the rest of the post... _________________ "I want to see gamma rays! I want to hear Xrays! Do you see the absurdity of what I am? I can't even express these things properly because I have to conceptualize complex ideas in this stupid limiting spoken language!" 

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aCOSwt Moderator
Joined: 19 Oct 2007 Posts: 2537 Location: Hilbert space

Posted: Sat Jun 22, 2013 11:03 am Post subject: 


LoTeK wrote:  did you study math, computer science or physics? 
Hmmm... didn't you claimed yourself an oldfashioned platonist ?
Then... well... I... simply once wanted to enter some place and something on the front door was written in some foreign language.
I, probably disgracefully, translated it into : "Let no one ignorant of Mathematics enter here"...
LoTeK wrote:  since 0 is a finite element in ℝ it's strange that we need infinity for the division by zero, isn't it? I mean if you want to take square roots from negative numbers you can construct ℂ and maybe there were some "problems" with i, but since a "real number" is either as imaginary as an "imaginary number" or an "imaginary number" is as real as a "real number" depending on ones philosophical position (platonism vs formalism vs contructivism etc), therefore I don't see any problem with ℂ, but if you need infinity for a division operation it's weird

I am not sure I fully understand what you mean.
Do you mean that the difference between a real number and a complex number is like a difference in opinion that could be reconciled , but the difference between 0 and infinite is a strong difference in nature that can in no way be reconciled ? _________________


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LoTeK Apprentice
Joined: 26 Jul 2012 Posts: 270

Posted: Thu Jun 27, 2013 7:18 pm Post subject: 


sorry for the late reply...
Quote:  Hmmm... didn't you claimed yourself an oldfashioned platonist ?
Then... well... I... simply once wanted to enter some place and something on the front door was written in some foreign language.
I, probably disgracefully, translated it into : "Let no one ignorant of Mathematics enter here"... 
hehe yes, I wanted to join the club too! but I think this spirit lives only in the underground nowadays, overrun by a horde of finance and insurance mathematicians...
Quote:  am not sure I fully understand what you mean.

I meant that there was a time when complex numbers were rejected by many mathematicians. They thought it's something weird and "imaginary". But if you are a constructivist then a real number or a natural number is imaginary too. On the other hand if you are a platonist then a complex number is as real as a real number, so there is nothing weird or problematic with complex numbers
Quote:  Do you mean that the difference between a real number and a complex number is like a difference in opinion that could be reconciled , but the difference between 0 and infinite is a strong difference in nature that can in no way be reconciled ? 
yes, I think thats what I want to say
The construction of the complex numbers are fruitful for engineers and for pure mathematicians, it's kind of simple, elegant etc. But those theories or constructions that extend the real numbers with an element "infinity" and then define 1 / 0 = infinity are neither fruitful in applications nor in pure mathematics (at least not as important the set of complex numbers).
so maybe from a strict formal point of view there are just fields, neutral elements, operations etc and the division by zero is not defined, no problem! but from a more conceptual / philosophical point of view there is still something wrong...
don't you agree? _________________ "I want to see gamma rays! I want to hear Xrays! Do you see the absurdity of what I am? I can't even express these things properly because I have to conceptualize complex ideas in this stupid limiting spoken language!" 

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Ahenobarbi Developer
Joined: 02 Apr 2009 Posts: 345 Location: Warsaw, PL

Posted: Thu Jun 27, 2013 7:50 pm Post subject: 


LoTeK wrote:  Thanks for the good answer, unfortunately you didn't say something I didn't know already (did you study math, computer science or physics?). since 0 is a finite element in ℝ it's strange that we need infinity for the division by zero, isn't it? I mean if you want to take square roots from negative numbers you can construct ℂ and maybe there were some "problems" with i, but since a "real number" is either as imaginary as an "imaginary number" or an "imaginary number" is as real as a "real number" depending on ones philosophical position (platonism vs formalism vs contructivism etc), therefore I don't see any problem with ℂ, but if you need infinity for a division operation it's weird (maybe I'm on the wrong way like those that didn't accepted ℂ ) 
It's weird to not have infinity in ℂ... When you have Rieman Sphere, why would you arbitrarily remove that one point from it? 

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LoTeK Apprentice
Joined: 26 Jul 2012 Posts: 270

Posted: Thu Jun 27, 2013 8:23 pm Post subject: 


I don't want to remove that point... why?
maybe when you have a rieman sphere it's weird to not have infinity, but when you use ℂ like real numbers than you don't have infinity, do you?
the infinity point isn't treated like all other elements in ℂ, is it? Moreover afaik 1 / 0 is defined, but not 0 * (infinity) for example?! _________________ "I want to see gamma rays! I want to hear Xrays! Do you see the absurdity of what I am? I can't even express these things properly because I have to conceptualize complex ideas in this stupid limiting spoken language!" 

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aCOSwt Moderator
Joined: 19 Oct 2007 Posts: 2537 Location: Hilbert space

Posted: Thu Jun 27, 2013 11:50 pm Post subject: 


LoTeK wrote:  sorry for the late reply... 
Please don't be!
Timeouts are only valid during exams, and exams are over!
LoTeK wrote:  I think this spirit lives only in the underground nowadays 
Not in the underground... just... behind the sacred fire, just as... it has always been.
LoTeK wrote:  overrun by a horde of finance and insurance mathematicians... 
Which is no more no less than what... *they* have always seen in the cave.
LoTeK wrote:  I meant that there was a time when complex numbers were rejected by many mathematicians. They thought it's something weird and "imaginary". But if you are a constructivist then a real number or a natural number is imaginary too. On the other hand if you are a platonist then a complex number is as real as a real number, so there is nothing weird or problematic with complex numbers 
Whatever you are, only incoherence and inconsistency are weird in maths. Period. As far as *all* the entities you use are used according to their definitions, *nothing* is weird.
This being said... and, hic & nunc off topic, I acknowledge there is something something weird in maths.
Very weird.
And all the people, *much more* clever than me in the field of Mathematics, I have had the chance to discuss with, acknowledged it as well :
Whatever trivial / highly complex calculus / demonstration you are achieving... the result... carries a level of... niceness!... Beauty?^H.
At the point that, writing the result, you are dead sure convinced that *it must be correct* and this just because it is nice !
Isn't that just the ultimate weirdness in the field of maths ? I think so !
Your certitude in the correctness of the result depends on... an... affect!
I'll elaborate... when this gets more on topic, I make no doubt that the reason for that is what justifies that I wrote the M of Mathematics in bold earlier.
LoTeK wrote:  The construction of the complex numbers are fruitful for engineers and for pure mathematicians, it's kind of simple, elegant 
elegant... hmmm... the term is used... appropriately!
BTW, my off topic is coming on topic... too quickly!
LoTeK wrote:  But those theories or constructions that extend the real numbers with an element "infinity" and then define 1 / 0 = infinity are neither fruitful in applications nor in pure mathematics (at least not as important the set of complex numbers). 
(not)fruitful ?
I personally cannot tell if that is fruitful or not.
And I just cannot tell that because... it is... : f u n d a m e n t a l !
Before speaking of infinity, let's just take something much more... simple ? : zero!
0, that you apparently admit without problem (or with less problems than infinity) can be seen very weird as a legal member of ℕ...
Hey ... any element of ℕ is prime exclusiveor nonprime, isn't it? ... 0 is... ? Neither prime nor nonprime !
0!=1
x^0 =1
What are these disgraceful / counterintuitive fiddlings ?
Of course these are completely useless, I will never ever ask my computer to compute 0! Useless &... Stupid!
So what are these fiddlings ?
Conventions !
And why do I need to resort to conventions, and these conventions in particular ?
In order to make *everything* coherent !
And why do I need to make so *everything* is coherent ?
In order to be able to... state universally !
No less !
What is the value of a statement I would make for x ∈ {1,2,12} ?
Nothing ! Worthless ! Useless ! This is a not fruitful mathematical statement.
Any statement valid for x ∈ {1,2,12} is... anecdotical ! Anecdotes are *not* maths !
What if I can state ∀x ?
Hey ! That is maths !
Maths work on pure concepts, concepts are generalizations, maths are all about generalization... maths are the... system (I did not write that word) of generalization.
0!=1 ; x^0 =1 ; 1/0=infinity are nothing but conventions.
Conventions needed to make *everything* coherent, this in order to enable universal statements.
That might not be considered fruitful, that is *huge*, that is fundamental.
LoTeK wrote:  so maybe from a strict formal point of view there are just fields, neutral elements, operations etc and the division by zero is not defined, no problem! but from a more conceptual / philosophical point of view there is still something wrong... 
wrong ?
I have noticed in your previous posts, that you have a clear and correct understanding of the difference between maths and physics.
However, I would guess that your vision of mathematics is the one of a physicist. (Absolutely no disrespect meant)
For the physicist, maths are at first a set of tools serving purposes. Mathematicians are enablers. Physicists trust in Einstein's relativity ? Therefore there must be something right in Minkowsky's geometry, therefore Minkowsky's geometry is fruitful.
This is nothing but the standpoint of utilitarianism. (Once again, no disrespect meant)
From the inside of mathematics : Minkowsky is right. Minkowsky is right... per se!
"From a more conceptual / philosophical point of view, there" just cannot be anything Wrong in maths.
There just cannot because, from a more philosophical point of view, maths are nothing but a perfectly regular... S...! (I managed not to write it) _________________
Last edited by aCOSwt on Fri Jun 28, 2013 9:44 am; edited 2 times in total 

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aCOSwt Moderator
Joined: 19 Oct 2007 Posts: 2537 Location: Hilbert space

Posted: Fri Jun 28, 2013 12:03 am Post subject: 


Ahenobarbi wrote:  It's weird to not have infinity in ℂ 
What's that ?
 It is definitely incorrect to have infinity in ℂ
 It is definitely incorrect to not have infinity in ℂ ⋃ {∞}
Period.
Edit : Ahenobarbi wrote:  When you have Rieman Sphere 
What's that ?
You *never* have a Riemann Sphere!
Depending on what you are working on, the Riemann Sphere is exclusiveor the Rieman Sphere is not !
Period. _________________
Last edited by aCOSwt on Fri Jun 28, 2013 10:04 am; edited 2 times in total 

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