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PAGE34, 3-1; Infinity borderline at 1*10^604 along with 1*10^-604, math's first precision definition of infinity/Correcting Math 5th ed
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Archimedes Plutonium
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PAGE34, 3-1; Infinity borderline at 1*10^604 along with 1*10^-604, math's first precision definition of infinity/Correcting Math 5th ed
Alright, I am now on chapter 3 of this 5th edition of Correcting Math. This chapter on "Infinity" is far and away the very worst mistake that mathematics needed to address since Ancient Greek times. The mistake of leaving finite versus infinite as mere crude notions and opinions and never a precision definition. It is rather funny how physics can advance so far by the 20th and 21st century by refining and precision understanding of the Atomic theory and what the atom is from its Ancient Greek Democritus Atomic theory. Yet in mathematics, Infinity was also around in Ancient Greek times, and never was there a equal refinement, understanding or making precise the finite versus the infinite. Infinity, today, is still the awful crude notion and opinion that Infinity was in Ancient Greek times.
It is as if physics went through a huge colossal enlightenment and renaissance while mathematics just went to sleep for 2 millenniums. And when mathematics finally woke up to its responsibility of a precision definition and meaning of finite versus infinite, they picked a crackpot mathematician of Cantor to fill the math books with fakery. Cantor does not define infinity as it relates to finite and thus sends the mathematics community off into a deadend of fakery for another 200 years.
But the story and history of infinity is a very long one and perhaps tied up with religion that makes it only come to a precision definition so late in the history of science. Religion loves infinity to be something nebulous, inchoate, fuzzy and never precise, because religion often devolves into supernatural and antiscience, which a infinity of "endlessness" is antiscience.
In the first decade of 2000 was infinity finally given its birthplace of what Infinity means-- a border on finiteness. All it takes is a "borderline between finite and infinite" and we have precision meaning of infinity.
There is psychology wrapped up in the history of infinity as well as religion, and perhaps it is a psychology religion mix that kept the truth hidden for 2 millenniums. What I am talking about here is the fact that mathematicians to this day even hate the idea of borders and borderlines in mathematics. We see this aversion, this antipathy by 4 Color Mapping of Appel & Haken. As sort of a instant rejection in mathematics of borders and if they can be thrown out, the mathematicians of that subject matter will throw out the borders. And you need not encourage them or give them any excuse to ignore borders, for they seem to delight in ignoring borders and tossing them out. We see it again in the Kepler Packing Problem, where borders are never accepted, yet borders are required in defining density of packing. So we see that mathematicians of the 20th and 21st century have mental psychological problems with borders and borderlines in mathematics, and these mathematicians would fail in the science of geography where borders are required and commonsense needed.
Now I suspect philosophy has waxed long and hard on the concept of infinity, and I wish I was more familiar with what philosophers of the past have written about infinity, whether a single one of them ever wrote about a simple idea, that finite moves or progresses and it moves and progresses to a point where finite reaches a border, a borderline or even a borderband, and that border stops the numbers from being finite once crossed and the numbers are now infinite numbers. Had any philosopher been wise enough to have had that idea? I suspect not, and even if that idea came up, it would have been fiercely resisted and opposed, because of the widespread notion of adding 1 more to any given number.
I am guessing that no philosopher ever wrote and waxed long on this idea of a border between finite and infinite, at least I never saw or heard of any such writings of the past. In this case, I can perceive of what would stop a person from ever exploring the idea that finite goes only so far and a border is reached and crossing the border you are in infinite number territory. The idea that was pounded in every young student of math, that suppose a number N is the last finite number, then you have N+1 which is finite and so there is no last finite number. But who is to say that N+1 is still finite?
And, such a argument of N+1, is not really valid if you put the whole entire knowledge of mathematics to bear, namely, the ideas of Huygens working on tractrix and pseudosphere about 1692 where he shows the area of tractrix equals the area of the circle of equal radius at infinity (or pseudosphere with sphere). Huygens, for the first time in math history gives us two objects, one of which has infinite stretch yet finite area. Something that should have been exploited and have caused our understanding of infinity to be centered on the tractrix. Because infinite reach of the Tractrix is still that of FINITE area. So by 1692, the great thinkers of math should have started a program of finding a Natural Borderline between finite and infinite.
But instead, in the history of mathematics, the community followed instead a crackpot of the late 1800s with Cantor's 1-1 correspondence as a substitute for borders.
An equal convincing argument in favor of a border, an argument I would be terribly and awfully surprised if no philosopher ever discussed, is that if there is no border separating finite with infinite, means, logically that the concept of finite and infinite is one singular concept and that everything is finite. So if you have a concept of finite with no border to cross into infinite, then you can never tell if any given number is finite or infinite. There is no infinity, if there is no means of telling whether finite or infinite. Only a border can separate the two and make the two distinct separate concepts. I have never seen anyone in books list that argument, perhaps it is because all of humanity hates and is averse to borders. Perhaps it is religion that makes all of humanity not want to have a borderline between finite and infinite, because it implies borders on God. They want to wish/pretend that the spiritual is borderless.
And we see this pitiful hatred of borders in modern day math where the quacks and flakes of mathematics constantly talk of "actual infinity" and "potential infinity", never reaching the heart of the argument or discussion-- a border between finite and infinite. Lazily putting off the work that must be done now-- find the Natural-Borderline between finite and infinite. Huygen's tractrix gives us the first clue, the motivation to find the border in the tractrix.
So, why in the history of mathematics, was there never anyone bright or smart enough to pick up from Huygens, way way back in 1692 and explore and further the tractrix, that as we move along the circle area of pi, that somewhere in the digits of pi we have zeroes in a row, perhaps not two zeroes in a row but three zeroes in a row would allow the tractrix to catch up in area and pinpoint a number which for the first time the Tractrix area actually equals the corresponding circle area at that spot, and thus, AT INFINITY is found. Why did all mathematicians ignore Huygens discovery and never develop it further, but rather, foolishly the math community picks up on Cantor in the 1890s and uses his fakery to model infinity? Is it that humans just have this horrible aversion to borders? Is it a religion-psychology mind curse on human minds? Or is it just simple foolishness and stupidity of humanity at large?
I need to talk more about the texture, the flavor, the nature and characteristics of infinity versus finiteness. Especially the idea that Infinity comes in two varieties, two flavors, two types, and they are the small infinity which the Huygens tractrix compared to circle area will discover, and we call it the infinitesimal infinity in calculus, and I call it the microinfinity. And then there is the other type of infinity-- the large scale infinity, the macroinfinity. This macroinfinity is the only type of infinity in Old Math. Those people were so blind in logic in thinking that infinity was only large infinity and that you cannot have a small infinity, so feverishly blind was Old Math and their silly stupid Cantor delusions. So what arguments could Old Math make for a microinfinity by a constant adding of 1 to save their finite counting numbers in large infinity? They never thought of that, that counting 1 more to a finite large number cannot save you from small scale infinity, the infinitesimal. But then, people in Old Math are not really scientists and logical people in the first place, since they just accept Cantor as if Cantor was the next chapter of the Bible, and not mathematics.
So, let us see how math, when clearly and logically done, discovers a NATURAL borderline in the digits of pi, a borderline that is the Microinfinity and thence we reverse it and say it is also the Macroinfinity borderline.
Very crude dot picture of 5f6, 94TH
ELECTRON DOT CLOUD
::\ ::|:: /::
::\::|::/::
_ _
(:Y:)
- -
::/::|::\::
::/ ::|:: \::
One of those dots is the Milky Way galaxy. And
each dot represents another galaxy.
. \ . . | . /.
. . \. . .|. . /. .
..\....|.../...
::\:::|::/::
--------------- -------------
--------------- (Y) -------------
--------------- --------------
::/:::|::\::
../....|...\...
. . /. . .|. . \. .
. / . . | . \ .
http://www.iw.net/~a_plutonium/ whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies
I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
Archimedes Plutonium
Alright, I am now on chapter 3 of this 5th edition of Correcting Math. This chapter on "Infinity" is far and away the very worst mistake that mathematics needed to address since Ancient Greek times. The mistake of leaving finite versus infinite as mere crude notions and opinions and never a precision definition. It is rather funny how physics can advance so far by the 20th and 21st century by refining and precision understanding of the Atomic theory and what the atom is from its Ancient Greek Democritus Atomic theory. Yet in mathematics, Infinity was also around in Ancient Greek times, and never was there a equal refinement, understanding or making precise the finite versus the infinite. Infinity, today, is still the awful crude notion and opinion that Infinity was in Ancient Greek times.
It is as if physics went through a huge colossal enlightenment and renaissance while mathematics just went to sleep for 2 millenniums. And when mathematics finally woke up to its responsibility of a precision definition and meaning of finite versus infinite, they picked a crackpot mathematician of Cantor to fill the math books with fakery. Cantor does not define infinity as it relates to finite and thus sends the mathematics community off into a deadend of fakery for another 200 years.
But the story and history of infinity is a very long one and perhaps tied up with religion that makes it only come to a precision definition so late in the history of science. Religion loves infinity to be something nebulous, inchoate, fuzzy and never precise, because religion often devolves into supernatural and antiscience, which a infinity of "endlessness" is antiscience.
In the first decade of 2000 was infinity finally given its birthplace of what Infinity means-- a border on finiteness. All it takes is a "borderline between finite and infinite" and we have precision meaning of infinity.
There is psychology wrapped up in the history of infinity as well as religion, and perhaps it is a psychology religion mix that kept the truth hidden for 2 millenniums. What I am talking about here is the fact that mathematicians to this day even hate the idea of borders and borderlines in mathematics. We see this aversion, this antipathy by 4 Color Mapping of Appel & Haken. As sort of a instant rejection in mathematics of borders and if they can be thrown out, the mathematicians of that subject matter will throw out the borders. And you need not encourage them or give them any excuse to ignore borders, for they seem to delight in ignoring borders and tossing them out. We see it again in the Kepler Packing Problem, where borders are never accepted, yet borders are required in defining density of packing. So we see that mathematicians of the 20th and 21st century have mental psychological problems with borders and borderlines in mathematics, and these mathematicians would fail in the science of geography where borders are required and commonsense needed.
Now I suspect philosophy has waxed long and hard on the concept of infinity, and I wish I was more familiar with what philosophers of the past have written about infinity, whether a single one of them ever wrote about a simple idea, that finite moves or progresses and it moves and progresses to a point where finite reaches a border, a borderline or even a borderband, and that border stops the numbers from being finite once crossed and the numbers are now infinite numbers. Had any philosopher been wise enough to have had that idea? I suspect not, and even if that idea came up, it would have been fiercely resisted and opposed, because of the widespread notion of adding 1 more to any given number.
I am guessing that no philosopher ever wrote and waxed long on this idea of a border between finite and infinite, at least I never saw or heard of any such writings of the past. In this case, I can perceive of what would stop a person from ever exploring the idea that finite goes only so far and a border is reached and crossing the border you are in infinite number territory. The idea that was pounded in every young student of math, that suppose a number N is the last finite number, then you have N+1 which is finite and so there is no last finite number. But who is to say that N+1 is still finite?
And, such a argument of N+1, is not really valid if you put the whole entire knowledge of mathematics to bear, namely, the ideas of Huygens working on tractrix and pseudosphere about 1692 where he shows the area of tractrix equals the area of the circle of equal radius at infinity (or pseudosphere with sphere). Huygens, for the first time in math history gives us two objects, one of which has infinite stretch yet finite area. Something that should have been exploited and have caused our understanding of infinity to be centered on the tractrix. Because infinite reach of the Tractrix is still that of FINITE area. So by 1692, the great thinkers of math should have started a program of finding a Natural Borderline between finite and infinite.
But instead, in the history of mathematics, the community followed instead a crackpot of the late 1800s with Cantor's 1-1 correspondence as a substitute for borders.
An equal convincing argument in favor of a border, an argument I would be terribly and awfully surprised if no philosopher ever discussed, is that if there is no border separating finite with infinite, means, logically that the concept of finite and infinite is one singular concept and that everything is finite. So if you have a concept of finite with no border to cross into infinite, then you can never tell if any given number is finite or infinite. There is no infinity, if there is no means of telling whether finite or infinite. Only a border can separate the two and make the two distinct separate concepts. I have never seen anyone in books list that argument, perhaps it is because all of humanity hates and is averse to borders. Perhaps it is religion that makes all of humanity not want to have a borderline between finite and infinite, because it implies borders on God. They want to wish/pretend that the spiritual is borderless.
And we see this pitiful hatred of borders in modern day math where the quacks and flakes of mathematics constantly talk of "actual infinity" and "potential infinity", never reaching the heart of the argument or discussion-- a border between finite and infinite. Lazily putting off the work that must be done now-- find the Natural-Borderline between finite and infinite. Huygen's tractrix gives us the first clue, the motivation to find the border in the tractrix.
So, why in the history of mathematics, was there never anyone bright or smart enough to pick up from Huygens, way way back in 1692 and explore and further the tractrix, that as we move along the circle area of pi, that somewhere in the digits of pi we have zeroes in a row, perhaps not two zeroes in a row but three zeroes in a row would allow the tractrix to catch up in area and pinpoint a number which for the first time the Tractrix area actually equals the corresponding circle area at that spot, and thus, AT INFINITY is found. Why did all mathematicians ignore Huygens discovery and never develop it further, but rather, foolishly the math community picks up on Cantor in the 1890s and uses his fakery to model infinity? Is it that humans just have this horrible aversion to borders? Is it a religion-psychology mind curse on human minds? Or is it just simple foolishness and stupidity of humanity at large?
I need to talk more about the texture, the flavor, the nature and characteristics of infinity versus finiteness. Especially the idea that Infinity comes in two varieties, two flavors, two types, and they are the small infinity which the Huygens tractrix compared to circle area will discover, and we call it the infinitesimal infinity in calculus, and I call it the microinfinity. And then there is the other type of infinity-- the large scale infinity, the macroinfinity. This macroinfinity is the only type of infinity in Old Math. Those people were so blind in logic in thinking that infinity was only large infinity and that you cannot have a small infinity, so feverishly blind was Old Math and their silly stupid Cantor delusions. So what arguments could Old Math make for a microinfinity by a constant adding of 1 to save their finite counting numbers in large infinity? They never thought of that, that counting 1 more to a finite large number cannot save you from small scale infinity, the infinitesimal. But then, people in Old Math are not really scientists and logical people in the first place, since they just accept Cantor as if Cantor was the next chapter of the Bible, and not mathematics.
So, let us see how math, when clearly and logically done, discovers a NATURAL borderline in the digits of pi, a borderline that is the Microinfinity and thence we reverse it and say it is also the Macroinfinity borderline.
Very crude dot picture of 5f6, 94TH
ELECTRON DOT CLOUD
::\ ::|:: /::
::\::|::/::
_ _
(:Y:)
- -
::/::|::\::
::/ ::|:: \::
One of those dots is the Milky Way galaxy. And
each dot represents another galaxy.
. \ . . | . /.
. . \. . .|. . /. .
..\....|.../...
::\:::|::/::
--------------- -------------
--------------- (Y) -------------
--------------- --------------
::/:::|::\::
../....|...\...
. . /. . .|. . \. .
. / . . | . \ .
http://www.iw.net/~a_plutonium/ whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies
I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
Archimedes Plutonium
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