AP's 25th book of Science-- Disproof of Riemann Hypothesis // Math proof series, book 11 by Archimedes Plutonium This is AP's 25th published book of science published on Internet, Plutonium-Atom-Universe
Archimedes Plutonium
AI Overview of AP's proof of Riemann Hypothesis.
"AI Overview says:: Archimedes Plutonium (AP) ..known for prolific..posts.. Usenet and dedicated Google Groups regarding 'Atom Totality' theory, which claims the universe is a single atom. AP is recognized .. claiming to have proven the Riemann Hypothesis and proposing 'new physics'.
Disproof of Riemann Hypothesis // Math proof series, book 11
by Archimedes Plutonium
This is AP's 25th published book of science published on Internet, Plutonium-Atom-Universe,
PAU newsgroup is this.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
Preface: The Riemann Hypothesis was a conjecture never able to be proven and for good reason, for it was the last symptom of a rampant disease inside of mathematics. Old Math did not have the true numbers that compose mathematics. Old Math had a rag-tag ugly collection of fake numbers with their Reals, their Negative numbers compounded with Rationals compounded with Irrationals and then adding on the Imaginary. These are fake numbers, when the true numbers of mathematics are the Decimal Grid Numbers. Because Old Math uses fake numbers, is the reason that a Riemann Hypothesis never is borne out of a fake number system and just languished, languished. You cannot prove something riddled in fakery. Below I demonstrate why having fake numbers in math, creates fake conjectures, and creates fake proofs, fake theorems, and creates a conjecture that can never be proven-- simply because the true numbers of mathematics are the Decimal Grid Number System. Quantum Physics proved in year 1900 with Planck that physics is discrete, not a continuum. But Old Math was too stupid of a community to follow physics example, and thus Old Math went deeper and deeper into the pit of dark falsehood with their Reals and ever more continuity and continuum.
Cover picture: Riemann Hypothesis deals with fake numbers of mathematics. When what is needed is the true numbers-- Decimal Grid Numbers. We learn Decimal Grid Numbers when very young, when just toddlers, wood counting blocks. All the true numbers of mathematics come from Mathematical Induction-- counting. Mathematical Induction is utterly absent in the Riemann Hypothesis, when it should be central to the hypothesis. There never exists a Riemann Hypothesis when the true numbers of mathematics are Decimal Grid Numbers.
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Table of Contents
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1) My history behind the Riemann Hypothesis disproof.
2) By 2011, I realized the Zeta functions were never equal in the Riemann Hypothesis.
3) True numbers of mathematics are Decimal Grid Numbers, a discovery by me in 2013.
4) True Numbers of mathematics are Decimal Grid Numbers and are discrete, not continuous for they have holes of empty space between one and the next number.
5) Old Math never well-defined Series equality, especially for Euler Zeta and Riemann Zeta.
6) My first disproof of Riemann Hypothesis as seen in 2016.
7) Subtraction Fallacy of Zetas.
8) By late 2023, I found a better explanation of the Subtraction Paradox with years of a calendar.
9) Was the Prime Number Theorem and Fundamental Theorem of Algebra, also fake conjectures and proofs?
10) Is there a Geometry disproof of the Riemann Hypothesis-- yes quite simple and easy!
11) Ongoing commentary and reflection back.
12) The Summary of Riemann Hypothesis and its Disproof.
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1) My history behind the Riemann Hypothesis disproof.
In the year 1991, after my discovery of the Plutonium Atom Totality in 1990, I assigned myself the task of proving the world's 10 worst outstanding conjectures. In 1991, I was eagerly writing the book on Atom Totality, but wanted some sideshow of math problems. For some reason, my mind gets fidgety if I work on only one problem. My mind is more at ease if I have several irons in the fire, all at once. So as I get stuck on one, my mind shifts to another.
Of course, well, I was a mathematician in training at University and that is what my degree was in, not physics. But the Atom Totality theory was pure physics, revolutionary physics.
I should briefly mention how I come to discover the Atom Totality theory, for all my science gushed forth after the Atom Totality theory.
In early 1970s, after 1972 graduating from University of Cincinnati with a degree in mathematics, and soon to be a teacher in mathematics, I set myself on a personal course challenge, to "mathematize the Darwin theory of evolution". Throughout my life I have given myself personal challenges, much like the one in 1991 to conquer the 10 worst math problems of the time.
Well I never expected to actually solve my first great challenge of mathematizing the Darwin theory of Evolution. What I mean by that is make evolution be like a mathematical formula or a mathematical geometry pattern.
And so, in the years 1972 through 1990, I kept reading books of science that may help, and of course physics books, looking looking for some key idea that could turn biology evolution into a math pattern.
To my amazement, I would achieve my long goal of mathematizing Darwin Evolution. It was a solution far far beyond the scope of my initial problem. I discovered the Atom Totality theory in 1990. I was surprised because I was working on a stock-market-business book and let my science efforts languish.
But sure enough, as I was making notes on physics, and that the Atom was pictured as electron dot cloud, and one night before bedtime looking at the stars overhead, my mind put 2 and 2 together. That the Atom was a Electron-dot-cloud, and the stars and galaxies was a dot-cloud. In my sleep I had come to the realization that the Universe was a single big atom, and the most pressing thing on my mind that morning was to ride my bicycle to the physics library and find out what chemical element fits best the Atom Totality-- it was plutonium to make the special numbers of 137 fine structure constant, pi and 2.71828....
Now the reader is not going to understand how an Atom Totality solves Darwin Evolution as being a math pattern or formula. But as I was writing the book in 1991 and doing math proofs on the side. I realized that the quantum theory of physics had a Superdeterminism in it. The John Bell Inequality where Dr. Bell talks about no free will in the universe. Today some call this quantum entanglement, but prefer Superdeterminism. Superdeterminism takes over on Darwin evolution and makes evolution be a rule rather than a science law or theory. Fate is what drives biological change in the math of quantum mechanics.
Still, surrounded by all these new ideas in 1991, I wanted a new challenge, and I chose to do the worst 10 math unsolved problems, and perhaps the biggest one on that list was the Riemann Hypothesis, RH.
The reason the RH was so big is because so many other problems of math hinged on whether RH was true or not true. Whereas most of the other unsolved problems were of the type that hoo hum, who cares.
So RH was also my most pressing of the 10, I selected. And as the months rolled by, and years rolled by I tackled more problems, so the list grew to 13.
But I solved most of the original list of 10 in the year 1991. However as the years rolled by especially after 1999 working on Logic, I discovered the method of Reductio Ad Absurdum was not a valid math proof method. And I had to go back to all those 10 proofs and see which were reductio method and either fix or admit I had no proof thereof. Sadly my Riemann Hypothesis proofs, I had two proofs of RH were Reductio Ad Absurdum-- proof by contradiction. I had to find a new method and say I had no proof of RH.
But then a fortunate discovery in 2013 as I was doing True Calculus textbook and discovered a geometry proof of the Fundamental Theorem of Calculus, FTC. I instantly recognized it as a proof of FTC, but only later realized it was a proof provided the true numbers of mathematics were Decimal Grid Numbers.
And herein, in 2013, I could go back to my RH proofs and solve them-- mind you, not to prove the conjecture, but the exact opposite, a disproof of the Riemann Hypothesis. RH was a false conjecture. It was not true, for it did not use the true numbers of mathematics.
And that is the reason no-one has ever proved RH. And no-one will, for the Reals and Complex are fake numbers.
When you have a mathematics, and of course you have to have numbers for mathematics. But if your numbers are fake numbers-- Rationals, Irrationals, Reals, Complex, if you have fake numbers. Your mathematics will one day come up with a mighty big conjecture, just as Riemann did in 1859 with the Riemann Hypothesis. And because you math is based upon fake numbers, that conjecture will never have a proof, nor can it ever have a proof because the system of numbers is all wrong and fakery.
So as I found this geometry proof of Fundamental Theorem of Calculus, the true numbers of mathematics need to be discrete numbers and the Decimal Grid Numbers are discrete. I found the world's first valid proof of FTC in 2013, and found that the true numbers of mathematics are discrete Decimal Grid Numbers.
Then, going back to Riemann Hypothesis, only I had no time to revise my proof in 2013. Going back in my mind, I realized when a day came and free of other work, I will write my 1991 RH proof as a Disproof of the Riemann Hypothesis.
So all in all, actually the most important proof AP ever made was the Fundamental Theorem of Calculus, for it completely destroyed RH and set it to right with a disproof.
Was RH a waste of my time in 1991?? Of course not, for I firmly believe the engagement, whether correct or incorrect, the engagement is the most important thing. For if not for the 1991 engagement, I probably would not have a disproof of RH today.
AP
Riemann Hypothesis in TEACHING TRUE MATH PROOFS by Archimedes Plutonium
2) By 2011, I realized the Zeta functions were never equal in the Riemann Hypothesis.
Definitely for sure, AP had a disproof by 2011 of Riemann Hypothesis, as the below posting shows, that by 2011, I realized the Zetas were never equal in RH. But then years later, after developing the Decimal Grid Number System, was I able to finally settle the issue on RH. For the RH is one of many problems of Old Math that were symptoms of the disease of "what are the true numbers of mathematics".
From: Archimedes Plutonium
Newsgroups: sci.math, sci.physics, sci.logic
Subject: ..the more important question of the Riemann Hypothesis
concerns the zetas!
Date: Mon, 20 Jun 2011 22:57:41 -0700 (PDT)
The more important question of the Riemann Hypothesis concerns the zetas.
This is June 2011, but back in May I wrote the below. What I discovered
back in May was that the Euler Zeta, the multiplication series
involving primes is larger, term by term than the Riemann zeta, as far
as I was able to inspect.
So one of the reasons that the Riemann Hypothesis, RH, is not a
mathematical conjecture at all, is because, we never are given a
precision definition of Series equality, along with no precision
definition of infinite versus finite.
So this leads to a more interesting question than the RH question of
the nontrivial zeroes. The more interesting question for mathematics
about the Euler zeta and Riemann zeta is the behavior of the zetas
term by term.
So we have several interesting possibilities involving the 603 digits
of pi.
(i) term by term the Euler zeta is always ahead of the Riemann zeta
out to the 603 digits and far beyond the 603rd digit
(ii) term by term the Euler zeta and Riemann zeta fluctuate back and
forth as being larger or smaller up to the 603rd digit of pi and beyond
(iii) never once, term by term is the Euler zeta equal to the Riemann
zeta up to 603rd digit and far beyond.
Now if I were forced to guess which is true, I would guess the Euler
zeta is always larger than the Riemann zeta, except when pi digits have more
than two zeroes in a row that the Euler zeta becomes smaller than the
Riemann zeta at those junctures, and the first one of those junctures
is the 10^603 or 603rd digit of pi. That is a guess, so do not hold me to account for
that. I am further guessing that no computer can straightforward check it, and
that only some tricks of analysis may give some clues. But the trouble
with tricks of analysis, is that it was tricks of analysis that got us
into this mess in the first place of thinking that the Riemann zeta
was equal to the Euler zeta.
It is mistakes and errors like this, of where several lousy definitions
or notions are cobbled together that we even entertain the idea that
the Riemann zeta is equal to the Euler zeta. Admittedly they come
close to one another, but every asymptote comes close to whatever
line-ray it is corresponding with. So what needs to be done in
mathematics on the RH, is to drop this senseless quest of the
nontrivial zeroes, and where they lie, but rather, let us
come back to the original first beginnings of the zetas and ask when
do they actually equal one another if ever, once we define equality as
being equal at some term by term basis.
Newsgroups: sci.math, sci.physics, sci.logic
From: Archimedes Plutonium
Date: Tue, 10 May 2011 22:19:32 -0700 (PDT)
Subject: Euler zeta Re: Computer data on pseudosphere and
10^603 as infinity
On May 10, 5:05 pm, Archimedes Plutonium
The above reminds me a lot of what I had done in April 2011,
From: Archimedes Plutonium
Date: Tue, 5 Apr 2011 11:22:13 -0700 (PDT)
Subject: Re: Euler zeta at quartic exp; Riemann Hypothesis is not a
math conjecture;
On Apr 5, 1:04 am, Archimedes Plutonium wrote:
> On Apr 4, 1:09 am, Archimedes Plutonium wrote:
> (snipped to save space)
> > =
> >
1.0823231912696857682736847489311912648699476995102564184784009090648683447
309\
> > 57590858261697449300912209644732005074539147200373592
> =
>
1.0823232269719986356222077948786718256055383764535625153845608734776218891
824
>
059875505900404487077591001611805526315478532126361381204565456019762008885
405
>
795033663773620009853356577688953398337652251650906951421869663804225781187
265
> 683682147691800078
> I had the Computer go out to the prime 199 to see if I could bump up
> that convergency to
> be 1.0824 rather than the reputed convergency of 1.0823.
Alright, the computer weighed in again by delivering what the first
46
terms of the Riemann zeta is
in exp4 to compare with the above
which is the 46th term of the Euler
zeta.
= {1, 1/16, 1/81, 1/256,
1/625, 1/1296, 1/2401, 1/4096, 1/6561,
1/10000, 1/14641, 1/20736,
1/28561, 1/38416, 1/50625, 1/65536,
1/83521, 1/104976, 1/130321,
1/160000, 1/194481, 1/234256, 1/279841,
1/331776, 1/390625, 1/456976,
1/531441, 1/614656, 1/707281, 1/810000,
1/923521, 1/1048576,
1/1185921, 1/1336336, 1/1500625, 1/1679616,
1/1874161, 1/2085136,
1/2313441, 1/2560000, 1/2825761, 1/3111696,
1/3418801, 1/3748096,
1/4100625, 1/4477456}
=
71603846070161235984974416572048882124033931427408513209760256918517060039/
66157745782864854606586051262785807972331951694504381871645179494400000000
=
1.0823199191999517184676148151103759569944513040893810814806532632698059273
Apparently the Euler zeta is larger than the Riemann zeta. Which is
strange to me for I would have guessed the Riemann zeta would be for
the longest time ahead of the Euler zeta.
But let us ask some questions about Riemann zeta, Euler zeta and
sphere, pseudosphere area. So we see the pseudosphere area always
appearing to lag behind the value of the sphere area. And it is my
claim that at 10^603 where pi is in stagnation of three zero digits
in a row, that the pseudosphere area catches up and overtakes the
sphere area for the first time.
So has anyone studied or payed attention to the Euler zeta versus
Riemann zeta as to the question of when one is larger than the other
term by term? It is easy to place the sphere and pseudosphere into
B matrices theory because the length of the arms of pseudosphere is
where we measure the area in 10, then 10^2 then 10^3 etc etc. However
for the zetas, B matrices can not be applied with meaning.
But there remains many questions such as whether they shift back and
forth as one zeta becomes larger than the other zeta or whether the
Euler zeta stays in the lead and remains there until a long ways out?
Now since pi is related to the primes and since pi has three zero
digits in a row for the first time at 10^603, one has to wonder if
something special happens with the Euler zeta and Riemann zeta at
10^603?
--- end quoting older May post ---
Archimedes Plutonium
3) True numbers of mathematics are Decimal Grid Numbers, a discovery by me in 2013.
Know what Numbers really are, not some sack of cobbled together junk in a junk pile called Reals.
History of discovery of true numbers of mathematics: can be pinned to the year 2013 where Decimal Grid Numbers replaces the Reals. I needed discrete numbers, numbers with holes or gaps of empty space from one number to the next, not a continuum. And by 2013, I started True Calculus, where I need empty space gaps between discrete numbers, in order for calculus to exist. Exist by proving the Fundamental Theorem of Calculus. This theorem is about showing that the derivative and integral are inverses of a function. The derivative is related to the integral, much as multiplication is the inverse of division, or addition is the inverse of subtraction, and vice versa. The only way, yes, the only way one can prove the Fundamental Theorem of Calculus, is by having discrete space, as seen in my book.
World's First Geometry Proof of Fundamental Theorem of Calculus// Math proof series, book 2
by Archimedes Plutonium (Author)
Last revision was 19May2021. This is AP's 11th published book of science.
Preface:
Actually my title is too modest, for the proof that lies within this book makes it the World's First Valid Proof of Fundamental Theorem of Calculus, for in my modesty, I just wanted to emphasis that calculus was geometry and needed a geometry proof. Not being modest, there has never been a valid proof of FTC until AP's 2015 proof. This also implies that only a geometry proof of FTC constitutes a valid proof of FTC.
Calculus needs a geometry proof of Fundamental Theorem of Calculus. But none could ever be obtained in Old Math so long as they had a huge mass of mistakes, errors, fakes and con-artist trickery such as the "limit analysis". To give a Geometry Proof of Fundamental Theorem of Calculus requires math be cleaned-up and cleaned-out of most of math's mistakes and errors. So in a sense, a Geometry FTC proof is a exercise in Consistency of all of Mathematics. In order to prove a FTC geometry proof, requires throwing out the error filled mess of Old Math. Can the Reals be the true numbers of mathematics if the Reals cannot deliver a Geometry proof of FTC? Can the functions that are not polynomial functions allow us to give a Geometry proof of FTC? Can a Coordinate System in 2D have 4 quadrants and still give a Geometry proof of FTC? Can a equation of mathematics with a number that is _not a positive decimal Grid Number_ all alone on the right side of the equation, at all times, allow us to give a Geometry proof of the FTC?
Cover Picture: Is my hand written, one page geometry proof of the Fundamental Theorem of Calculus, the world's first geometry proof of FTC, 2013-2015, by AP.
Whenever you have a science, and you see "cobbling together of items"-- means the science is primitive, riddled with error and half-truths, and such was the Reals of Old Math.
The True Correct Numbers needed, in order to do Math or any science like physics; cannot be done with fake numbers of Reals, Irrationals, Complex.
4) True Numbers of mathematics are Decimal Grid Numbers and are discrete, not continuous for they have holes of empty space between one and the next number.
Alright, once we have Logic, we start mathematics, and the best place to start is how we recognize and use numbers. Math has two houses, one is Geometry and one is Numbers (Algebra). We can start with either one of them, geometry or numbers. Here we start with numbers.
Decimal Grid Number System is the only true number systems and the only system to be used in science, especially physics. For in physics quantum mechanics they deal with a Discrete space and mass and energy for that is what quantum means, -- discrete and in year 1900 with Planck on forward in physics was all quantum mechanics. But the naive and stupid in mathematics kept pressing on with their silly continuum, such as Cohen with the Continuum Hypothesis.
The smallest Decimal Grid Number System is the 10 Grid and is shown here as this.
9.0, 9.1, 9.2, 9.3, 9.4, 9.5 9.6, 9.7, 9.8, 9.9, 10.0
8.0, 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9,
7.0, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8, 7.9,
6.0, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9,
5.0, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9,
4.0, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9,
3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9,
2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9,
1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9,
0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9,
You see, there are holes and gaps from one number to the next. And in 10 Grid, those 100 numbers excluding 0 are all the numbers that exist in 10 Grid. Every number in 10 Grid is created from Mathematical Induction by adding 0.1 onto 0 and keep adding 0.1 until we reach 10.
Then we have the 100 Grid built from mathematical induction on 0.01, then the 1000 Grid built from mathematical induction upon 0 by adding 0.001 until we reach 1000. And so on for every higher Grid System.
This is a decent and sensible way of developing the true numbers of mathematics. In Old Math during the time of Euler and Riemann, any foolish and silly person can come into the shop-of-mathematics and plop down onto the table of math a bag of numbers and insist it is part of mathematics.
In New Math, we do not allow such silly actions of making crackpot bags of numbers and saying they are part of mathematics. In New Math, all numbers come from Mathematical Induction on the initial starting number of 0, and only grid systems of 10, 100, 1000, 10000, etc.
Now this is important that we have the true numbers of mathematics, for we are going to show that the Riemann Hypothesis erred in thinking they had equality of the Euler Zeta series with the Riemann zeta series. And that was never true. So if the Euler Zeta never equaled the Riemann Zeta, well, you no longer have a Riemann Hypothesis, and hence a disproof of Riemann Hypothesis.
5) Old Math never well-defined Series equality, especially for Euler Zeta and Riemann Zeta.
Let us focus some more on Numbers, how to represent them, for in how to represent numbers can either destroy our understanding or allow us to understand fully and clearly. If we have the wrong representation of numbers, we cannot hope to fully understand them.
In the history of mathematics, one of the key discoveries was the Decimal Number System. It was discovered in Ancient times by Hindu Arabic, but was slowly accepted and needed many changes along the way to our modern day use. But, even as of recently, 2017, most math professors, perhaps all except AP, thought that Number Systems never change the value of numbers, regardless of what system you use. And in the age of computers, the computer electronics favors binary system, with its electronic gate open or closed.
The Binary system is 1, 10, 11, 100, 101, 110, 111, 1000, etc and those represent, 1,2,3,4,5,6,7,8 in decimals.
Trouble is, though, one number system is superior to all other number systems, the decimal system superior. And the representation of numbers, does in fact, affect the values of numbers, except decimal. Decimal Number system is the only system that does not affect the actual true value of the number. How can that be? It is the fractions that are distorted in other number system, not decimal.
The decimal number system is the only non-corrupting system, and all other systems have failures of number values, in the fractions.
The reason Decimal is superior, is because of the 231Pu Atom Totality demands a number system that has Clean-Pure Numbers as border endpoints. A clean-pure number is this progression.
1
10
100
1000
10000
etc
and
.1
.01
.001
.0001
etc
Now, here is what I wrote for 13 year olds as a lesson and a proof of why Decimal Grid Numbers are so very very special and unique in all of Mathematics, so that True Math is based on Decimal Grid Numbers.
Date: Mon, 18 Mar 2019 23:05:24 -0700 (PDT)
From: Archimedes Plutonium
To: Plutonium Atom Universe <plutonium-a...@googlegroups.com>
Subject: Series never given a well-defined- equality
Disproof of Riemann Hypothesis-- why it is not a piece of mathematics but only at best a approximation rule.
Alright, I need to assemble all these examples of mathematics where the Proof or demonstration is really a Approximation of Numbers and not an equality of numbers. Thus, the proof or demonstration is never a theorem or truth of mathematics but really just a "rule".
(1) Algebra of .999... not equal to 1 but is always a tiny bit short of 1
(2) Oresme's harmonic series 1 + 1/2 + 1/3 + 1/4 +. . not divergent but truly convergent with infinity borderline
(3) Prime Number theorem, not a theorem but a rule
(4) Fundamental Theorem of Algebra, not a theorem for it is not even mathematics when it uses negative numbers, rationals (most of them are not numbers but incomplete divisions), irrationals, imaginary. The only true numbers that exist are Grid Numbers.
(5) Riemann Hypothesis, not a true bit of mathematics and is in the same boat as Prime Number theorem for the zetas are never ever equal, but rather a close asymptotic approach of one another. The zetas are not equal and thus RH is a rule of mathematics, never a truth or theorem.
Prime Number Theorem proof done via Math-Induction, posted in 2015 in sci.math.
Mathematical-Induction Proof of Prime Number Theorem PNT.
In New Math we have Grid Systems for the true numbers of mathematics, and we no longer
have Reals or Complex.
10 Grid
100 Grid
1000 Grid
10^4 Grid
10^5 Grid
10^6 Grid
etc
Primes, the actual count of Primes in those Grids listed above follow this progression
This is the Grid Progression.
10 4 actual primes, 10/2 = 5 predicted when using the formula of base sqrt10 is exponent 2
10^2 25 actual 25 Spot on Exact with sqrt10 base 100/4 which Here is 4
10^3 168 actual lower bound 1000/7 = 142,
upper bound 1000/6 = 166 Here 6
10^4 1,229 actual lower bound 10,000/9 = 1111 ,
upper bound 10,000/8 = 1250 Here 8
10^5 9,592 actual lower bound 100,000/11 = 9090 ,
upper bound 100,000/10 = 10,000 Here 10
10^6 78,498 actual lower bound 1,000,000/13 = 76,923 , Here 13
upper bound 1,000,000/12 = 83,333
10^7 664,579 actual lower bound 10^7/16 = 625,000 ,
upper bound 10^7/15 = 666,666 Here 15
10^8 5,761,455 actual lower bound 10^8/18 = 5,555,555
, upper bound 10^8/17 = 5,882,352 Here 17
10^9 50,847,534 actual lower 10^9/20 = 50,000,000 , Here 20
upper 10^9/19 = 52,631,578
10^10 455,052,511 actual lower 10^10/22 = 454,545,454 , Here 22
upper 10^10/21 = 476,190,476
10^11 4,118,054,813 actual lower 10^11/24 = 4,116,666,667 , Here 24
upper 10^11/23 = 4,347,826,087
10^12 37,607,912,018 actual lower 10^12/26 = 38,461,538,46- Here 26
upper 10^12/25 = 40,000,000,000
Series representation of Actual Primes rather than Progression representation
4 + (25-4) + (168-25) + (1229-168) + (9592-1229) + . .
Progression of Predicted primes from formula using base sqrt10
10/2 =5, 100/4 =25, 1000/6 =166.666.. , 10000/8 = 1250, . .
Series representation of Predicted Primes using Formula sqrt10 as base with its exponent
5 + (25-5) + (166.666..- 25) + (1250 - 166.666..) + . .
Actual Infinity Borderline is 1*10^604 but since that is cumbersome to work with and since no computer has ever calculated the actual-primes from 0 to 1*10^604 we Pretend infinity border is 1*10^4 and use that via Math-Induction to find the Doctored Formula.
Mathematical Induction Proofs to tell if two different Series are equal to each other at infinity requires these items:
1) Starting Equality
2) Mid Section of N to N+1 provided by Grid System
3) Ending Equality at the infinity border
Here we pretend 10^4 is the infinity border and look to find a Doctored formula of base sqrt10 exponent that delivers and Ending Equality.
10^4 Grid has actual 1229 primes yet predicts 10000/8 = 1250
So we Doctor our Formula of base sqrt10 exponent to use pretend Grid 10^4 where N is 4 exponent on 10000/8 and subtract actual primes of Grid N-2 (that is 10^2 Grid) and add actual primes of Grid N-3 ( which is 10 Grid). So we have arithmetic wise, we have 1250 - 25 + 4 = 1229.
So we have in the end here, we have a Starting Equality of 100/4 = 25 primes in 100 Grid and we have a Ending Equality of 10000/8 subtract 25 add 4 = 1229.
Now, we apply that Scheme or Pattern to the true infinity borderline of 1*10^604 and so we have something like this 10^604/1208 subtract Grid N-2 add Grid N-3 or add Grid N-1 add Grid N-2.
We do whatever it takes to Doctor the formula so that it makes the End result equal to actual primes at infinity border.
Now, we have a starting equality 100/4 and a Doctored End Equality. Now we do not worry about applying the Doctored Formula on the Mid Section terms, for we certainly have to apply that doctoring. Just so long as we have the Start and End terms agree with actual Prime Count.
Now, let me show you this method on the Zeta Series of the Riemann Hypothesis and show you why they are never equal for no starting-equality is possible nor a equality at infinity. Show you on the Harmonic series (Oresme) and why it never diverges. And show you on the reciprocal two series of 2-doubled compared to triangular numbers alleged to converge to 2, why they are not equal at infinity border since it is impossible to doctor them at infinity border for a Ending equality. However, on the reciprocals we can find a different series for each that does converge at infinity border and hence are equal series.
What I am developing here is the first time in math history that we clean up the concept of two different Series equaling each other. This has never been done before for the simple reason that when you have Infinity as a notion, mere notion and opinion as to what infinity is, you cannot have a concept of Series equality at infinity. Only when you have a precise infinity with a borderline, can you have precision Series understanding.
Note of caution to readers, in that the proofs shown of 2015 and 2016 are in Old Math, where I just did not use Grid Numbers solely, still using the fake Reals and Complex. Neither the Prime Number theorem nor the Fundamental Theorem of Algebra are not true in New Math. New Math is only Grid Numbers and PNT and FTA would not come up for even a discussion of a proof. Because in New Math, primes have no formula. And the FTA would not come up because there is just one and only one solution to a polynomial in New Math, regardless of the degree of that polynomial.
Newsgroups: sci.math
Date: Sun, 21 Feb 2016 11:43:29 -0800 (PST)
Subject: ..Proof of Fundamental Theorem of Algebra
From: Archimedes Plutonium
..Proof of Fundamental Theorem of Algebra
Fundamental Theorem of Algebra
Since this proof is long, I decided to split it into three parts. And there is something special about the Riemann Hypothesis, Prime Number Theorem and Fundamental Theorem of Algebra, in that all three require a proof by Mathematical Induction and this is because every major theorem using numbers must have a underlying Math Induction proof since numbers themselves come directly from the Peano axioms of the Naturals based on Math Induction. Math Induction is the only powerful means of proving conjectures whose scope is so broad and vast, and using numbers. Math Induction proof is the only proof method outlined in the Peano Axioms themselves and so, it is reasonable to think that our most general and sweeping conjectures would require a proof method by Math Induction.
Editing & Commentary corner: The issue of whether a set is algebraically closed or complete, is not related to the question of continuity which everyone in Old Math blindly thought. Algebraic closure or completeness is related to whether Mathematical Induction exists over that set in question. It is via Math Induction that we know a set is closed-complete.
Summary of text: All mathematicians have heard of the famous saying-- "Give me the Counting Numbers, and all the rest of algebra is just definitional add-ons", (or words to that effect by Kronecker). Well, mathematicians all liked that statement but they never really heeded it, or understood it fully, because if you understand it, means that algebraic completeness and algebraic closure comes from Mathematical Induction, and not from the irrelevant and silly side show of a continuity argument. To prove an orange, we do not go out and prove an apple.
In New Math, Algebraic Closure and Completeness is a byproduct of a overarching Mathematical Induction upon a set of numbers.
Proof Text
_________________________
Counting Numbers Completeness & Closure Proof
_________________________
We define Completeness-closure by its most primitive Algebraic structure and that comes from the Axioms of the Counting Numbers circa 1889 with Dedekind-Peano, specifically the Successor axiom with the Mathematical Induction axiom.
The Counting Numbers are the set 1, 2, 3, 4, 5, . . .
So, Completeness & Closure and being able to have Mathematical Induction on a set of numbers is identical in these proofs. In Old Math, they resorted to the opinion that completeness and closure meant continuity, or had everything to do with continuity. Strange, very strange twist of illogic, to think that Completeness and Closure meant continuity, when those two concepts are utterly foreign to one another. And, if anyone had asked those old rascals what does continuity have to do with the Counting Numbers and Rationals and yet those two sets are Complete and Closed, would have realized how illogical it is for a mathematician to think that a pursuit of continuity means completeness and closure.
Now in the proof of Fundamental Theorem of Algebra, I am going to equate Completeness with the concept of Algebraically-Closed. Old Math never really distinguished the difference between completeness and closure, but what it means is that given a set of operators and given a set of numbers, are there numbers missing. An example of that is sqrt-1 would be a missing number if not included in the sets of numbers. Another example is that if math had only one operator, addition, then the Counting Numbers would be the only set of numbers in mathematics, but since we have four operators, subtraction, multiplication, division, we have other numbers. So that numbers, are complete and closed with respect to operators is the fundamental theorem of algebra.
So the proof for Counting Numbers is very short and sweet in that it is just to restate those axioms of Successor with Mathematical Induction. But we have to include a detail of something that is more general than the "polynomial equation" used in the Old Math of the Fundamental Theorem of Algebra with complex numbers of D'Alembert in 1746 with Gauss in 1799 and also, indirectly with Dedekind cut for Reals in 1872.
Also, important is that the Counting Numbers are axioms that require only the operator addition and needs no multiplication operator. When we include division as an operator upon Counting Numbers we get the Rationals, and when we include division upon integers we get the Rationals. When we include multiplication and division upon Rationals we get the Infinite-Numbers as Irrationals with their roots such as sqrt2 or sqrt-1 or sqrt-2 as examples.
Finally when we do Union of sets of Rational with Irrationals we get the NewReals.
So, what we do for Completeness proofs, we go far beyond D'Alembert and Gauss who were stuck on polynomials and stuck on continuity, is make the more general case of given the progression of Number sets:
1) Counting Numbers from addition
2) Rationals from division on Counting Numbers
3) Infinite Numbers called Irrationals (two types of root-irrational and transcendental-irrational) from multiplication and division on Rationals
4) Union of Irrationals with Rationals, a countable set all begot from Mathematical Induction is the set of NewReals
Sometime ago, I used to write this proof discussing Reals and Complex numbers with imaginary "i". I no longer can do that because nearly all of that is phony math. The only numbers that exist in New Math are the Rationals and unioned with the Irrationals and every number besides Rationals are Irrationals that cover the space in-between rationals.
I have to discuss the Fundamental Theorem of Algebra from first beginnings-- the Counting Numbers. And look how silly Old Math was that never even gave the slightest idea that for a proof of completeness-- can only begin with the completeness of Counting Numbers.
I have to also inject the infinity-borderline upon those four listed sets above. So not only were the definitions illogical of completeness, algebraically-closed, continuity, but there was a problem of applying the infinity borderline to numbers.
The infinity borderline is 1*10^604 for macroinfinity and for microinfinity or the infinitesimal it is 1*10^-604 and the algebraic closure of these numbers is 1*10^1208 and its inverse. The infinity borderline is derived in two methods, one, by algebra it is derived from where pi digits are evenly divisible by 120=5! and its square, and second, is derived from the fact that when pi has its first three zeroes in a row, 10^-601, 10^-602 and 10^-603, the area of the tractrix equals the area of the associated circle for the first time, and since Huygens proved the area of tractrix equals associated circle at infinity, we have a borderline.
So that 1*10^604 is the last and largest finite number, and all numbers beyond are infinite-numbers and all numbers smaller than 1*10^-604 (except 0) are infinite-numbers since 1*10^-604 is the smallest nonzero positive finite number.
So, the proof that Counting Numbers are a Complete set is that they have both Successor and Mathematical Induction. The Counting Numbers have a Math-Inductor Element and it is the number 1, so given 0 and 1 adding 1 to 1 gives 2, adding 1 to 2 gives 3.
The next larger set on our list is the Rationals.
_______________________
Rationals Completeness Proof
_______________________
To prove the Rationals form a Complete set in terms of Algebra, or algebraically closed set, we must show that a Successor function and a Mathematical Induction exists upon that set.
Here, the proof requires an Infinity-borderline, which the Counting Numbers did not require that, because the Counting Numbers had the Successor axiom along with Mathematical Induction axiom. So for Rationals, we need to prove that there is a Math Induction Element that retrieves all Rationals.
To prove Rationals are Complete or Algebraically closed, as these dots of finite points evenly spaced is to prove that this set has Mathematical Induction.
^
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. . . . . . . . . .
. . . . . . . . . .
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So, all I need to prove is that Rationals have a Successor with Mathematical Induction. Since the set of positive Rationals is
{ 1*10^-604, 2*10^-604, 3*10^-604, . . , (1*10^604 -1), 1*10^604}
We see it has a Successor and Math Induction using the inductor element of
1*10^-604. All the Rationals are an induction of 1*10^-604. Same argument for the negative Rationals.
_______________________
Irrationals Completeness Proof
_______________________
To prove Irrationals are a complete and closed set, I need to show a Math-Inductor Element. Here I use the Grid Systems of 10, 10^2, 10^3, etc etc where I pretend each Grid is the infinity borderline so that 10 is the infinity border in 10 Grid and 100 is infinity border in 100 Grid, etc. Then I go out further in the Grids of 3 decimal place values of Grids, so that for 10 Grid I go out to the 10^4 Grid and use the 1*10^-4 as the Math Inductor Element to fetch all the Irrational Infinite Numbers that lie between the Rationals of the 10 Grid. This set of Irrationals of 10^4 Grid would be
{ .0001, .0002, .0003, . . , 9999.9999, 10000} Now in this set the Rationals of 10 Grid are deleted (.1, .2, .3, .4, . . , 9.9, 10} leaving a set of Irrationals Infinite Numbers.
_______________________
NewReals Completeness Proof
_______________________
The NewReals would be the set that is the Rationals unioned with the Irrationals. In the Grid System, it would be the set of 10^4 Grid { .0001, .0002, .0003, . . , 9999.9999, 10000} without deleting the 10 Grid elements.
This NewReals set in any Grid would be countable and listed as every number of the set and hence Mathematical Induction is placed upon that set.
_________________________________________________________
Fundamental Theorem of Algebra Completeness Proof or Algebraically Closed of Rationals unioned with Irrationals (infinite-numbers)
_________________________________________________________
First, let me note that the imaginary and complex number and the Complex Plane are just Infinite-Numbers and where sqrt-1 is an irrational number represented by 9999..999d where d is decimal point of a number which has 1208 digits of 9s, just as the irrationals are also infinite-numbers such as sqrt2 is just 1.415 in 10^2 Grid in pretend infinity border is 10^2 and where we borrow the 1.415 in 10^3 Grid since 10^604 is too cumbersome to write.
So in New Math, either a number is a Rational or a Infinite-Number which we call irrationals. The Irrationals are Space-fillers, for they fill the space between rationals or beyond rationals.
Let me define Infinite Number-- an infinite number requires more digits than the allowable 604 digits rightward of the decimal point or more digits than the allowable 604 digits leftward of the decimal point. In the Grid Systems, where we pretend the infinity borderline, we also pretend infinite-numbers as the Space-filler, since working with 1*10^-604 is way too cumbersome.
Now if you look at the Cartesian Coordinate Plane it is just dots of finite points evenly spaced with mostly empty space between those dots, and empty space is the region occupied by infinite-numbers, the irrationals.
So in Pretend Infinity to be 10^3 because it is cumbersome for 10^604, that the Rationals would have points of 1.414 while lying just next to 1.414 are the Infinite-numbers of 1.4142 and 1.4143, what used to be called sqrt2 in Old Math as irrational-number and complex number of sqrt-2, are in New Math all just simply Infinite-numbers. The sqrt-1 is the infinite-number sqrt9999..99d, and the number sqrt-2 is the infinite-number sqrt9999..98d, where there are 1208 of 9s digit in -1 and 1207 of 9s digits in -2.
So, now a proof that FTA is Complete that given any polynomial has solutions, is too narrow, because we needed no polynomial test to show Counting Numbers and Rationals are complete and algebraically closed, so why put that test to Infinite-numbers? The only true test is whether the Infinite Numbers have mathematical induction and thus an inductor-element.
An example will show what I mean.
Sqrt10 in pretend infinity of 10^3 is 3.1624 which gives us 10.000. First we take the sqrt 10 as 3.16227766... Then we take successive sqrt10, first sqrt10.01 = 3.1638.. then sqrt10.001 = 3.1624.. then sqrt10.0001 = 3.162293.. Notice that in 10^2 Grid of sqrt10.01 we had to go to 10^3 Grid to obtain 3.163^2 = 10.0045.. where we truncate the "45.." to get what we wanted 10.00. So an irrational number (an infinite-number) draws upon a higher Grid in order to get the desired Rational number of the lower Grid. So, all irrational numbers are infinite numbers because they have digits beyond the infinity borderlines. And a Conjecture was proven called the 2 Digit Place Value Conjecture that states that the borrowing need no more borrowing than 2 Digit Place Values to obtain the root of a irrational polynomial root.
So, what we have for Rationals and Irrationals unioned to form NewReals combined as a set of numbers in Fundamental Theorem of Algebra is a Mathematical Induction on Grid Systems. If a Grid cannot get us the root-irrational number, we have to go to a higher Grid and borrow. And the 2 Digit Place Value Conjecture requires no more than 2 higher Grids, but we insist on 3 Digit Place Value because pi has 3 zeroes in a row before 10^-604 place value.
So, is there a Successor and a Mathematical Induction Element upon all these numbers of Rationals unioned with Infinite numbers? Yes, because the Infinite Numbers-- the irrationals are all able to be listed in order, in other words, Grid Systems obey Mathematical Induction.
Now, the question comes, is there any higher set than the Rationals unioned with Infinite Numbers, or does Completeness stop with the Infinite Numbers and Algebraic Closure stop with 10^1208 Grid? That is like asking is the Euclidean Plane full when it has Rationals and Infinite-Numbers occupying the space between Rationals? Is there anything more to the plane once we have dots of Rationals with their empty space in between the dots as Infinite-Numbers? The answer is the plane is full and there is no higher set than the Infinite Numbers.
6) My first disproof of Riemann Hypothesis as seen in 2016.
Riemann Hypothesis disproof, first posted of a disproof in sci.math 2016, although the suspicions were rampant already by 2011 as seen in first post above.
Newsgroups: sci.math
Date: Fri, 12 Feb 2016 21:34:34 -0800 (PST)
Subject: Major Logical Flaws & Disproof of the Riemann Hypothesis
From: Archimedes Plutonium
AP's Proof of Riemann Hypothesis, part 1 of 2
PART 1 of 2: Logical Flaws & Disproof of the Riemann Hypothesis
Major Logical Flaws & Disproof of the Riemann Hypothesis RH
by Archimedes Plutonium
Introduction:
Comparing RH to the Prime Number Theorem PNT, in that proof Mathematical Induction on Series, I had a Starting Equality of 100/sqrt10^4 and using sqrt10 base rather than "e" base I have a Starting Equality of 100/4 = 25, and at infinity I Doctor the Ending Equality.
Now, we compare Riemann Hypothesis with its zetas and we also compare the Harmonic Series. The Zetas and the Harmonic Series are never able to give us a Starting Equality to apply a Math Induction proof of RH. What that means is RH is unprovable. It is a false conjecture.
The reason that Riemann Hypothesis is always a failure, is because the two series of Zetas are never equal to each other term per term, because they lack a Starting Equality to form a proof by Mathematical Induction. The Prime Number Theorem is provable because it has a Starting Equality of 100/sqrt10^4 where we have 100/4 by replacing "e base" with sqrt10, and although the prediction count by using sqrt10 is far more sloppy than other formulas based on "e", there can never be a Starting Equality with "e".
The way to prove PNT or RH is via Math Induction, with a Starting Equality and let the Grid Systems be the Math Induction format of "if N then N+1". and at the Infinity borderline wash away the imperfections for a Ending Equality by Doctoring or by tacking on more terms to Equilabrate each series at infinity. This can be seen in the Proof of the Prime Number Theorem. So long as we have a Starting Equality, we can prove PNT.
Why do the Zetas never equal each other but rather-- asymptotically approach one another? It is because they both have BadFractions such as 1/3 = .333... which the 3 digits go beyond the infinity borderline and never able to be tamed into a Starting Equality. Unlike what are GoodFractions 1/8 = 0.125000...
The Logic of the Mechanics of RH proof: the logic here is that RH should parallel the proof of the PNT. Not that Prime Number Theorem is equivalent to RH, but parallel in proof structure.
I have never compared PNT to RH and how RH should be proved using PNT in parallel concert.
Both PNT and RH have huge problems with Series, but it did not stop PNT from having a proof.
Convergency Theory precisely defined:
Convergency theory, and what we have is a less strict form of equality. In math we have equality but also we have convergency to make two concepts, each distinct from one another converge to equality at infinity via Math-Induction on series. Not asymptotic approach of two different series.
Convergency boils down to five items:
i) starting equality terms of two items in comparison
ii) Middle terms close together by a lower and upper bounds factor, a "if N then N+1" which is demonstrated by the Grid System.
iii) the terms near the infinity borderline and are either Doctored of formula or are tacked on terms to Equalibrated both series.
iv) the final terms of the two items in comparison are equal "at infinity"
v) convergency has a very close similarity to how Mathematical Induction works in that a starting equality, a ending equality and we say all the terms in the two items under comparison are "convergent equal" in the Middle section
However, I do see a huge problem in a ** starting equality ** for the Zetas. I managed to find starting equalities in PNT such as the primes from 0 to 100 are 100/4 where the 4 is begot from using (sqrt10)^4 rather than using "e log".
So, I see huge problem in getting a Starting Equality for the Riemann and Euler Zetas.
So, what I suspect is going to happen is that a proof of PNT is possible because these conditions are able to be satisfied but not satisfied for the zetas of RH.
The RH was invented in a time period of 1800s where infinity was ill-defined and never well-defined and so was the theory of Series. So that the RH was solid Old Math with foggy notion of infinity and a infinity without a border between finite and infinite, so that a Oresme series of 1 + 1/2 + 1/3 + 1/4 + . . in Old Math was considered Divergent, of course because infinity was a screwy notion of "forever without any borders". In New Math, the borderline is found to be 1*10^604 and so Oresme's Series is a finite number Convergent series as should be all Fractional Term series converge. We see from Grid Systems where we pretend that 100 is infinity border that 100 terms in the Harmonic Series 1+1/2 + 1/3 + 1/4 + . . + 1/100 would converge to approx 5 or thereabouts so that 5% of 100 as infinity border indicates that the larger powers of 10 as infinity border would have a decreasing percent for convergence. So, in Oresme to Euler and Riemann with their ill-defined infinity they would have thought the Harmonic Series diverges when in fact it converges. That effectively puts an end to a proof for RH.
The subject of Logic was never really all that big during the time of both Euler and Riemann and they had errors of logic in their thinking and published work which today's modern day mathematicians have never come face to face with.
So Equality of Series is similar to Mathematical Induction, in that you need a starting case, and then you assume "n" and if "n+1" is true, then the set is equal to the Counting Numbers. For the Zetas, we never have a Starting Equality.
Similar to the Prime Number Theorem of the accounting of the abundance of primes. The formula Li(x) is terribly close to equaling the amount of primes, but it too suffers from never having a starting equality, because the logarithmic function Ln can never give equality. So when I replace Li(x) with sqrt10 as basis, we see that for 100/4 where the 4 is (sqrt(10))^4 gives exactly 25 primes from 1 to 100. So we have a Starting Equality and at the Infinity borderband we can engineer a ending equality and so we have equality of amount of primes with the formula Sqrt10 basis.
7) Subtraction Fallacy of Zetas.
Alright, now for the subtraction fallacy, as if the "never equality for the zetas" was not punishing enough.
Let me now walk through the exact error of logic, the second fatal flaw of RH and why the zetas are never equal due to the subtraction fallacy, and why the Riemann Hypothesis is phony.
Missing Dollar Fallacy:
I do not know how old is the Missing Dollar Paradox, whether it is just a recent 20th century knowledge, and I suspect so. The important thing about that Paradox is that mathematics easily goes astray when you have the infinite series, and you have subtraction involved. Because it is very difficult to reckon the "basis for any subtraction with infinite terms". But if anyone is in doubt that Euler and others committed this fallacy, simply needs to look at the Euler zeta compared to the Riemann zeta and realize, that although they approach one another asymptotically, they never actually become equal, just as the tangent function never actually meets or intersects or equals at x=pi/2 for division by zero is undefined. The zetas never equal, not because of division by zero, but simply due to the fact that the Euler zeta is always larger.
Three soldiers go to a hotel in World War 2 before deployed to Europe. They sign in and each pays $10 for their room. The owner comes in and sees he has 3 soldiers going to Europe so sends the bellman up with $5 in singles and says give them back this money. The bellman is rather corrupt and also cannot divide 5 by 3 evenly so decides to give each soldier back just $1 and pocket the $2. So, what is our accounting? Well each soldier payed $9 for his room for a total of $27 and the bellman pocketed $2 so where is the missing $1?
The resolution of the above paradox involves a true frame of reference. If we say the three paid 25 for their room was returned 1 each and the bellman pocketed 2 is a correct math of 25+3+2. Another correct math is to say each paid 9+1/3 for their room which is 9.333... x 3 is 28 with the bellman pocketing 2. But in the paradox if you make the frame of reference as 3 x 9 = 27 with 2 to the bellman you are in trouble. The same paradox appears in Riemann Hypothesis to get a equality of Euler Zeta with Riemann Zeta.
If we look at page 102 to 103 of Derbyshire's Prime Obsession book of 2003 we see a subtraction involved in infinite sum series. On page 103, Derbyshire says this: "When subtracting the left-hand sides, treat (1-(1/2^s)Z(s) as a blob, a single number (which of course it is, for any given s). I have one of this blob, and I have 1/3^s of it."
In the below old post of mine, I discussed the fallacy of what I call "Misplaced Subtraction". In that dollar fallacy, if you subtract 1 from 10 and then have 9x3= 27 and with the 2 you end up with 29, so where is the missing dollar? If you properly do the arithmetic, 25 was paid and so 25+3 = 28 with the bellman pocketing 2. It is this fallacy, that Euler committed and which Riemann and later followers would not correct, but rather use the flawed math.
So, on page 102 we see Derbyshire with the Riemann zeta and for my purpose I will use the terms of just Z = 1 + 1/2 + 1/3 for those three are sufficient to reveal the Logical Error of Euler. When I add 1+1/2 +1/3, I get 1.83333...
And when I multiply by 1/2, I get 1/2Z = 1/2 (1.83333...) which is nothing wrong yet. However, it is the subtraction that the fallacy catches those unaware, unsuspecting. It is the Misplaced Subtraction that makes the Riemann zeta never equal to the Euler zeta.
So, on page 102 where Derbyshire has this, only reduced to my example at hand:
(1 - 1/2) Z = 1 + 1/3 + 1/5
And adding 1+1/3 + 1/5 is not going to be 1/2(1.8333...) but rather is that of 1.5333... or, if I included the next terms of 1/7 then 1/9 etc etc, nowhere am I going to get 1/2(1.8333...). And the reason being, well, is quite simple, in that the Fallacy of Subtraction of Series, just as the Missing Dollar Fallacy (Paradox).
When you do subtraction in mathematics, you have to be very careful of what "base" you subtract from, so that if you subtract 1 from 10 to get 9 and 9x3=27 when you should have subtracted 5 from 30 in the Missing Dollar Paradox below.
Well, in the Hotel Fallacy, the error is to never acknowledge the 25 platform, the frame of reference, of what the soldiers paid, but rather to think that the only platform is the 30 platform, so that when subtracting or adding with only 30 in mind, the fallacy creeps into the accounting. Same thing with the Euler & Derbyshire accounting that as you treat these "blobs" you treat the Zetas as only a infinity platform with no other platform to consider. And that causes the error.
Euler and all his future followers made that same fallacy with the zetas. It is an easy mistake to make, especially when you have two infinite series. And especially when you have division coupled with subtraction as in the Euler zeta. Now below is an old post of April 2011 where I talk about this Euler mistake and point to the page 102 starting in the Derbyshire book. When you subtract that second series from the first series, you no longer are guaranteed equality. For example of the Missing Dollar:
3 x $9 was paid and the bellman pocketed $2 = 27 + 2 does not equal 30
$10 + $10 + $10 = $30
So the error of Euler is that he needed to first establish an infinity border, and say he finds it to be 10^604. Then, his Riemann zeta of additive terms is smaller than 10^604 and is a specific finite rational number. Now when Euler multiplies by 1/2^s the equations are still equal, but, when Euler (via Derbyshire) subtracts the two equations, there are two different and separated Accounting Basis and so they are no longer equal in the subtraction.
For example in the Missing Dollar Fallacy:
3x9 = 27 add on 2 is 29 and not 30
First accounting basis 25 in the till + 1 + 1 + 1 for each soldier + 2 for bellman = 30
Second accounting basis 25 in till + 2 for bellman = 3 x 9 for soldiers
In the first accounting our infinity border is 30 and in the second accounting our infinity border is 27
Yet Euler in his proof had 30 = 27 or had 30 = 29.
AP writes: The theme of this post is that Numbers in Old Math are decayed and fake, and is a gaggle collection of rot that should never have been assembled together. The true numbers of mathematics all comes from Mathematical Induction, and not a conglomerated mess of a dab of numbers here, another dab of numbers there. Mathematical Induction is the only means of creating Numbers and are the Grid Numbers
0, 1, 2, 3, 4, 5, 6, . . .
0, .1, .2, .3, .4, .5, . . , 9.9, 1 as 10 Grid
0, .01, .02, .03, . . , 99.99, 100 as 100 Grid
0, .001, .002, . . , 999.999, 1000 as 1000 Grid
.
.
.
0, 1/(10^604), . . , 1*10^604 as the 10^604 Grid and is the last finite number Grid for beyond 1*10^604 are all infinite numbers and its inverse.
When mathematics uses fake and decayed numbers, then it starts to generate conjectures and hypothesis, for which there are never any proof because the numbers are so fake and decayed that you end up with Rules and Approximations and asymptotic close approaches but never equality. Mathematics is about Equality, not approximations. For that reason, the Riemann Hypothesis is a piece of junk, a fake conjecture. When you use the real true numbers of mathematics, you see RH for what it is worth-- a rule, a close approach approximation, just as the Prime Numbers are a close approach to x/Ln(x) but never equal in 2.71... and only once equal in base sqrt10.
Comment: now it is often heard in math circles that we need, need, need a proof of RH for so many things of math are dependent upon a true RH. And what I have to say about that-- is those urgent calls for a proof of RH are calls by featherweights of mathematics who are so dumb in math, they never saw the ellipse is never a conic and to this day, deny the oval is the slant cut in cone, not the ellipse. So it is featherweights like that who think RH is so important, when RH was never a piece of true math in the first place.
8) By late 2023, I found a better explanation of the Subtraction Paradox with years of a calendar.
A common mistake in math Subtraction and how to be vigilant and guard against.
Archimedes Plutonium
Dec 24, 2023, 8:47:49 PM
to Plutonium Atom Universe
Add to my 25th book of science-- Disproof of Riemann Hypothesis, for my version below is a different but abbreviated version of the Hotel Paradox and it is so easy to make this mistake in subtraction. The remedy below is that I needed to start with a nonpublishing year of 2018.
On Sunday, December 24, 2023 at 6:57:45 PM UTC-6 Archimedes Plutonium wrote:
So here I am nearly into 1January 2024. I started publishing books in 2019, and as of now have 268 published books (actually 1 was denied publication).
So doing routine math subtraction that is 2023 - 2019 = 4. And 268 / 4 = 67 books per year, which is far more than 1 book per week.
On the other hand if we count the years we have 2019, 2020, 2021, 2022 and 2023 which is 5 years, not 4 years.
So where is this math paradox coming from. And could some theoretical math such as the Riemann Hypothesis have this paradox embodied, enshrined into it.
It appears math subtraction has a flaw not unlike the paradox of division by 0. And perhaps division by 0 is related to this flaw of subtraction.
AP
As excellent of an example of the Subtraction Paradox from the Hotel story is. As the years passed by since publishing this book in March of 2019, my 25th published book of science, in the ensuing years I found an even easier story to tell of the Subtraction Paradox. Those of us in mathematics know of the division problem or paradox, that you cannot divide by zero or you tear up all of mathematics. And since subtraction is related to division, for division is simply "fast subtraction", while multiplication is fast addition. Since division has a paradox, that subtraction must have some form of paradox. And that paradox in subtraction is **where do we start to subtract?**.
As the Hotel story shows, the true subtraction starts with subtract 5 from 30, the bellman gives 1 dollar to each soldier, and pockets 2 dollars making 25+1+1+1+2 = 30. Whereas the incorrect accounting is subtract 3 from 30 is 27 and the bellman keeps 2 is 27+2 = 29.
In the ensuing years since publishing this book in 2019, I found an even easier subtraction story to tell. One day I was figuring out how many books I had published divided by how many years I had been writing those published books. I started in year 2019 writing books and publishing them and by year 2023, the end of 2023, I had published my 269th book of science. (A minor exception in that my 259th book was censored and not able to be published since it was about a resolution of the Israel-Palestine Conflict, censored and blocked from publication).
So, here is an easier and perhaps finer example of the Subtraction Paradox. If I subtract 2019 from 2023 I get 4, as in 4 years of publishing 269 books of science. Yet the true years are 5 years for we must include 2019 also.
I wanted to know this statistic as to see the rate of writing books and how much time elapsed. So 269/5 is 53.8 books per year, which is slightly more than 1 book written and published per week. That is an awful grueling schedule and pace.
But I recognized in my calculating, I remembered back to writing the Riemann Hypothesis disproof with its Hotel Paradox. I had find an easier story to tell of how subtraction can lead one astray.
For example, this year is now 2024. And suppose I started take vitamin D pills in 2016. How many years have I taken vitamin D pills? A novice would do 2024 subtract 2016 equals 8 years of taking vitamin D. A more circumspect person would count on his fingers 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023, 2024, and come up with the correct answer of 9 years.
Same goes for the Riemann Hypothesis, their subtraction of series is fakery and so their entire math is false.
9) Was the Prime Number Theorem and Fundamental Theorem of Algebra, also fake conjectures and proofs?
Date: Wed, 20 Mar 2019 12:26:18 -0700 (PDT)
From: Archimedes Plutonium
To: Plutonium Atom Universe <plutonium-a...@googlegroups.com>
Subject: what RH teaches us-- the numbers of Old Math are fakery
What RH teaches us-- the numbers of Old Math are fakery. And teaches us that Old Math never had a Well Defined Definition for Series equality.
On Sunday, March 17, 2019 at 1:35:41 PM UTC-5, Archimedes Plutonium wrote:
I need to re-investigate the Riemann Hypothesis and that also means another look at the Prime Number Theorem, Fundamental Theorem of Algebra. I have to check if those survive when Mathematics has Decimal Grid Numbers as the true numbers.
And it is the technique of Doctoring I spoke of earlier that saves the Prime Number Theorem, saves the Fundamental Theorem of Algebra, and others. The use of Doctoring in Mathematical Induction.
Alright, I am certain that the RH was never a theorem of mathematics, for it dealt with fake numbers. When you have mathematics all about true numbers-- Decimal Grid Numbers, then you never have any problem with .999.... is never equal to 1. And you never have any problem with the Harmonic Series of Oresme of 1 + 1/2 + 1/3 + 1/4 + ... + for that series is always convergent, never divergent. Then you come to Prime Number Theorem, and it is not a theorem of mathematics but a Approximation Rule.
And that makes total sense, because on one side of the mouth of a mathematician, he is saying there is no formula for all the primes, yet on the other side of the mouth of that same mathematician, he is saying Primes are equal to a formula x/Ln(x), so our mathematician is a hypocrite on that score.
And then we come to the Fundamental Theorem of Algebra which uses all the numbers of Old Math, their decayed, smelly, putrid gaggle of collection of numbers. An ugly theorem and a fake theorem is FTA. It is a hornswaggle, not a proof and not a truth of mathematics.
Finally we come to a conjecture that just would not be solved as the fakes of Oresme series, the fake of .999... = 1, the fake of Prime Counting. No, RH could not be molded into a "acceptable theorem" for its fakery was too much to hornswaggle.
The zetas are never equal. The zetas do approach one another, but that does not mean they are equal.
So, what the Disproof of RH tells us, and teaches us, is that the true numbers of mathematics are the Grid Numbers. And all of Old Math has to be tossed out the window.
Also, the question of Completeness of Numbers when the numbers are Grid Numbers is a rather silly question, because the only numbers that exist are a progression starting with the unit base, so in 10 Grid .1 is unit base and keep adding .1 to arrive at 10, in 100 Grid .01 is unit base. So Mathematical Induction forces completeness. Another avenue into completeness is the concept All Possible Digit Arrangements, and Grid Numbers do that, for every number is generated in a Grid and creates All Possible Digit Arrangements.
What the Riemann Hypothesis teaches mathematics and all sciences-- check to see if your numbers or assumptions are the true numbers or assumptions, otherwise you go for centuries without ever having a proof.
UPDATE, 18MAR2020, I am reflecting back over the past year of my writing the TEACHING TRUE MATHEMATICS series, for age 5 all the way to age 26 in Graduate School. And I discovered in that writing that every math professor worth his weight in salt, knows that the primes have "no pattern". Most will admit the primes have no pattern, no one formula. But every mathematician except AP, cannot admit to himself/herself that the concept of "prime number" is untenable. For you have the Counting Numbers built from addition. Everyone who knows logic, well, knows logic really well, knows that you cannot define a number as prime, if you have no "operation of division" when you define Counting Numbers. This is a point of logic that flies over the heads of all mathematicians except AP. What I mean is-- look at the Grid Numbers System, there is no concept of "prime number" in that system. Because Grid Numbers are actually built not just from a addition operator, but also they have a division operator. In the 10 Decimal Grid, we stop at the "scale number 10" (see what Scale Numbers are in AP's books, 10, 100, 1000, etc) and as we stop there we divide it into 1 and now we start the entire 10 Decimal Grid System with 0, and then add 0.1 and successively add 0.1 until we reach 10. In Decimal Grid Systems, no such thing exists as a Prime Number. There are no primes in Decimal Grid Systems. For Counting Numbers alone, have no division operator upon them, and this is why Primes in Old Math never had a formula. You cannot have a formula on a concept that does not exist for Counting Numbers have no division operator.
When you do mathematics and are lacking in a logical mind, then you find out that you have the Counting Numbers built without a division operator, and then you see some numbers like 2,3,5, 7, and your first dumb impulse is to think there is a concept that is prime and legitimate. Then you work in mathematics for 20 years in school and come to realize Primes never have a pattern, and why should they, for they are built from a logical viewpoint of addition operator but no division operator. That is the reason primes have no pattern, for you are not doing mathematics at all, you are engaging in the error of thinking you have a legitimate concept of "prime". Then you spend your whole life in mathematics, thinking there is a legitimate conjecture called the Riemann Hypothesis. If true, RH puts some order into the Prime numbers. And that is a folly of one folly over another folly.
Can there be a RH for Grid Number Systems? Sounds absurd because real true math is only Decimal Grid Numbers and none of negative numbers, rationals, irrationals, reals, complex-- all of those are fakery numbers. Prime numbers are fakery numbers. So, can one even get started on a RH of Decimal Grid Numbers? No, because RH in Old Math is a colossal house of cards of fakery.
So, I ask any and every mathematician of Old Math-- you all know that Primes have no order, no formula. Yet here, you chase after a RH which puts some order into Primes. So, I ask you, do you not think you are a hypocrite, and not a mathematician. Because you admit freely primes have no order, and yet on the other hand, you spend an entire life chasing after RH which says primes have order.
What RH teaches mathematicians and the world at large, RH teaches how silly contradictory are the minds of most mathematicians.
10) Is there a Geometry disproof of the Riemann Hypothesis-- yes quite simple and easy!
In mathematics geometry, there are graphs of asymptotes. These are curvedstraightline figures as a chain or string of tiny fine straightlines that approach a full straightline but never intersect. Never intersect even at infinity equals 1*10^604 or its inverse 1*10^-604 nor 0.0.
We define an asymptote as a curvedstraightline figure that approaches a full straightline figure such as the x-axis or the y-axis.
And a function that has not been fully converted into a polynomial over a specific interval is the candidate function of Y= 1/x for it is an asymptote for the y-axis and a asymptote for the x-axis. The Y= 1/x approaches but never intersects with either axis, x or y axis.
And the reason that asymptotes is a disproof of the Riemann Hypothesis is that both the Euler Zeta and the Riemann Zeta can be taken as one as Y= 1/x and the other as y-axis and x-axis. Euler Zeta never intersects with Riemann Zeta, are never equal to each other from 0 out to infinity, never are equal. And hence the Riemann Hypothesis is dead on arrival.
11) Ongoing commentary and reflection back.
Archimedes Plutonium
Oct 29, 2021, 12:40:50 AM
to Plutonium Atom Universe
With my recent work on the 6 paradoxes of math operators, time to revise my Riemann Disproof for the subtraction paradox is one of the reasons Riemann Hypothesis is a erroneous conjecture.
Archimedes Plutonium
Oct 30, 2021, 2:50:49 PM
to Plutonium Atom Universe
It is appropriate time for AP to revise his DISPROOF of the Riemann Hypothesis. Appropriate for I feel in peak prime logical condition at this time in my life. Ever since I saw that 9 times the muon rest mass is 945 and sigma error means the real electron of atoms is the muon with proton being 840 MeV and not Old Physics 938 MeV means I am in such pinnacle peak logic shape that I can now revisit the Disproof of Riemann Hypothesis and amplify the clarity. Amplify the reasoning that Riemann Hypothesis is a piece of worthless junk, a rotten stinking mess of mindless mathematics.
Is there any other idea in the history of science that can compare to the stinking mess of Riemann Hypothesis? Yes, long ago there was the idea that Earth was flat for the senses said that if Earth was round we would fall off this globe. And so a flat Earth was seen to be accepted for thousands and thousands of years. And the pinnacle peak of flat Earth was to say-- "Well, if Earth is flat, something has to hold flat Earth up and here we have the idea of a giant turtle holding up Earth or a giant elephant". The giant turtle holding up Earth is the Riemann Hypothesis of mathematics.
So the pinnacle peak of a horrible idea that Earth is flat is a giant turtle. And in mathematics the horrible idea was numbers as a continuum of Reals and Complex, and the pinnacle peak of that horrible idea of math of a continuum and the wrong numbers for mathematics, comes in the form of not a turtle or a elephant, but comes in the form of a Riemann Hypothesis, RH.
RH conjecture is when a subject like mathematics has ingrained horrible ugly ideas, ideas that are wrong and worthless and in error-- a continuum and Reals and Complex. And so as Old Math keeps all these errors, those errors rise to a pinnacle peak hypothesis called the Riemann Hypothesis. But there never is a proof of RH, simply due to the fact that it is built from error filled math ideas.
RH today is like someone proving the giant Turtle or giant Elephant is holding up Flat Earth.
Archimedes Plutonium
Oct 31, 2021, 4:21:00 PM
to Plutonium Atom Universe
The Zetas are never equal to each other.
Old Math thought that they could have 1/x equal to either the x-axis or y-axis.
When you think about it, the Riemann Hypothesis is a statement that an asymptote equals the straight line it is approaching, but the asymptote never intersects that line. Yet Old Math saying they are equal.
Archimedes Plutonium
Oct 31, 2021, 5:11:20 PM
to Plutonium Atom Universe
I should have a long commentary summary in this book, for the Riemann Hypothesis was still the largest single challenge in mathematics in the decade of the 1990s, early 2000s. Not until 2013 when AP sees the #1 challenge in all of mathematics was never the Riemann Hypothesis, but rather was the geometry proof of the Fundamental Theorem of Calculus, which by 2013 was discovered by me that you need geometry and the numbers of mathematics to have holes and gaps between one number and the next number. You needed empty space between one number and its successor number, for without empty space, you have no calculus.
I am going to post this Riemann Hypothesis to sci.physics along with sci.math, for those in physics can learn a extremely important lesson from the fakery that was Riemann Hypothesis.
Although Physics entered 1900 with Max Planck discovery of Quantum Mechanics and the Planck constant, entered the 1900s on a great sound logical note, realizing Space is discrete in quantum mechanics, while the mathematicians on the other hand, wasted the entire century of 1900s with their mindless foolery of pursuing even greater and larger continuums, as seen by Cohen. And it took from 1900 to 2013 with AP's discovery of a geometry proof of Fundamental Theorem of Calculus to finally debunk the continuum of Old Math, but to also show why Riemann Hypothesis was mindless foolery.
Math is now free of its mindless foolery of continuum, but physics in that time of 1900 to 2013 and even today is full of another mindless foolery-- General Relativity, dark matter, dark energy, Big Bang, black holes, neutron stars, worm holes, .... and a huge list of utter fake nonsense. Just a few days ago I was watching a TV program of NOVA of "Universe Revealed: Age of Stars" and for the life of me, it was like watching a NOVA show where they were saying the Earth is flat and some big turtle underneath Earth was holding it up. That bad was this NOVA show that it should be seen as sci-fi comedy.
So physics although it was elite in thinking logical in year 1900 with Max Planck leading the way into Quantum Mechanics, that physics had its own disastrous folly of logic with General Relativity and leading the century into goofball trash of Big Bang, black holes, dark matter, dark energy, worm holes, neutron stars and this myriad plethora of plain old ugly garbage science.
The entire century of 1900s to 2013 was lost in math, with its continuum and Riemann Hypothesis, when, what the center of attention should have been in mathematics was give a Geometry Proof of Fundamental Theorem of Calculus. That should have been the center of attention in all of mathematics from 1900 to 2013. Instead, it was the error filled Riemann Hypothesis.
In Physics, they started the century off in a spectacular grand style with Planck's Quantum Mechanics, but soon it fizzled out into the obnoxious low down stupidity of General Relativity and black holes then dark matter dark energy. When, what should have happened is that Maxwell's Equations should have been the center of attention throughout the 1900s along with quantum mechanics. This happened on a tiny small scale with Feynman's quantum electrodynamics. But the goofball worthless physics of General Relativity dominated the 1900s and is still in force today as seen in that wretched NOVA show of "Universe Revealed: Age of Stars".
The lessons to be learned from the Riemann Hypothesis, is that physics can go down into insane foolery just as easily as math went into insane foolery from 1900 to 2013.
If, I say if, in a big way. If the main thrust of physics had been electricity and magnetism throughout the 1900s, along with its quantum mechanics. Under that circumstance, it is highly likely that someone in the physics community would have seen that Dirac's magnetic monopole of 1930s was actually JJ Thomson's 0.5MeV particle and that the newly discovered muon by Anderson and Neddermeyer was actually the true electron of atoms. And the true proton of atoms is a 840MeV proton torus doing the Faraday law with the muon inside the torus thrusting through the proton to produce electricity and more magnetic monopoles.
But when mathematics is under a mirage and delusion of Riemann Hypothesis, all of math suffers.
Same thing for physics, when they are under a mirage and delusion of General Relativity, Big Bang, black holes, dark matter, dark energy, there is little hope of any true physics coming out of that cesspool physics.
Archimedes Plutonium
Nov 1, 2021, 1:58 AM
to Plutonium Atom Universe
As my memory goes, I discovered the Plutonium Atom Totality theory on 7 November 1990, while living in Hanover New Hampshire and eager to rush to the library that day to see for sure it was plutonium, not some other element.
Months after Nov1990 were spent in writing up the theory and publishing in newspapers and a copy to US Library of Congress. It was now 1991, and what I did next surprises me to this day. I turned my attention to solving all the big math problems of that time. And there was no bigger math problem than the Riemann Hypothesis in 1991. I did every major unsolved math problem of the time, everyone that was known to me. And by 1993, I had access to Usenet, to start spreading my ideas world wide. The below post was one of my very earliest ever and mentions the Riemann Hypothesis. In those early days, I loved to give two proofs of these outstanding conjectures, not just one proof but two. A style of mine that has carried with me to this day.
Back in 1991 my legal name was Ludwig Plutonium. And in those early years of 1990s I was so proud of the Atom Totality theory that I wanted to continue the celebration.
Newsgroups: sci.math
From: Ludwig.P...@dartmouth.edu (Ludwig Plutonium)
Subject: Wiles blunders
Message-ID: (CBo3E...@dartvax.dartmouth.edu>
Date: Thu, 12 Aug 1993 22:20:39 GMT
Lines: 51
Tabloid presses press for stories like that of apprentice A. Wiles--
" Wiles Masters The Cold Fusion Reporting Technique". Wiles has 1000
pages which 5 other math majors S. Kochen, K. Ribet, H.M. Edwards, B.
Mazur, and J. McKay can read. What has the world come to, when an
alleged proof is reported as a forgone conclusion because 6 persons
jump-up-and-down? Can not the NYT staff recognize self-deluded
publicity seekers? What is the limit for math tolerance? When one
person from Princeton reports a 10000 page proof and the method of
proof is-- readers fatigue. The most important aspect of a math proof
is to convince. If Wiles really does have a valid 1000 page proof,
then it can be boiled-down to 1 or 2 pages. Wiles can not do that,
indicating his proof is another fake. Here are the logical flaws in
Wiles's alleged proof. 1) Elliptic curves can not uniquely represent
the positive integers 2) Wiles can not even produce Pythagorean
triples when the exponent is 2. 3) Fourier Analysis proves that all
generalized functions are uniquely representable by sine-cosine. But
after transforming Wiles's elliptic curves into the more general
mathematics of Fourier Analysis, the net result is that when Wiles
wants to show the nonexistence of peculiar elliptic curves, his
method implies that the sine-cosine function of Fourier Analysis
does not exist. 4) Wiles's method contradicts Fourier Analysis.
5) Wiles's method is indirect nonexistence. Mathematically there
are only three viable existence proof methods i) direct existence
ii) direct nonexistence iii) and indirect existence. A proof
method of indirect nonexistence is impossible. The supercomputer
4-color mapping problem proof is another fake proof because it
uses the method of indirect nonexistence. See The Dartmouth
19MAY1992 for my two proofs of the 4-color mapping problem.
Forgive these 6 math majors for they are weak in mathematical
logic and know not what they do. And be not surprised that some
in the math community will eject overboard sine-cosine just to
embrace wiles curves. Wiles is wily about publicity, but will
he be a test-tube-cry-baby once he realizes that his FLouT sunk?
Not all is lost though, because Wiles's blunders creates a very
important mathematical conjecture. Call my conjecture
Complementary Mathematics (CM) since it originates from the
complementary principle of quantum physics. CM states: Math
theorems have a duality of proof method, either geometrical or
arithmetical, where one excludes 100% of the other
(particle-wave duality of quantum mechanics). Hence, the
correct geometrical proof of FLT will come only after someone
gives the proven equivalent geometrical statement to the
arithmetical FLT. The Moebius function proved to be the
geometrical equivalent to the Riemann Hypothesis. See my two
proofs of the Riemann Hypothesis The Dartmouth 9AUG1991, and
my proof of FLT The Dartmouth 16APR1991. The arithmetic
proofs of both the Riemann Hypothesis and FLT were achieved
through the uniqueness of the number 2. But the geometrical
proof of FLT will come only after the equivalent geometrical
statement is obtained, and it will be much longer than my 1
page proof of FLT, or my 1 paragraph proof of the World's
most outstanding math problem-- the Riemann Hypothesis. This
newsgram was published in The Dartmouth under Notices 9JUL1993.
Sincerely, LP
----------------
Newsgroups: sci.math
From: Ludwig.P...@dartmouth.edu (Ludwig Plutonium)
Subject: Re: 1 page proof of FLT; this is what Fermat
had in mind when he wrote "margin to small". Fermat
reasoned that the proof was so simple that others would
easily rediscover it.
Message-ID: (CBrGJ...@dartvax.dartmouth.edu>
References: (CBpno...@dartvax.dartmouth.edu>
(1993Aug14.0...@husc14.harvard.edu>
Date: Sat, 14 Aug 1993 17:57:14 GMT
Lines: 14
Fermat reasoned that the proof was so easy, so simple that
others later would see it and not worth Fermat's time.
Fermat saw the uniqueness of the number 2 the only number
in all of math where its sum equals its product allowing
for the construction of a P-triple when exponent is 2 but
when exponent is 3 or greater there are no numbers where
sum equals product. A 1 page proof too long for Fermat's
margin.
The uniqueness of 2 also proves the Riemann Hypothesis
when the Euler formula--multiplication of terms, call it
E and the zeta function--addition of terms call it Z,
when E subtract Z equals zero only real component 1/2
works otherwise there must exist another number in math
such that n+n+n=nxnxn (for exp1/3) This is just a sketch
of my one paragraph proof of the Riemann Hypothesis anyone
wanting the full proof I will gladly email.
ludwig.p...@Dartmouth.edu
--------------------------
Newsgroups: sci.math
From: Ludwig.P...@dartmouth.edu (Ludwig Plutonium)
Subject: TWO PROOFS OF THE RIEMANN HYPOTHESIS
Message-ID: (CBtM4...@dartvax.dartmouth.edu>
Date: Sun, 15 Aug1993 21:52:54 GMT
Lines: 144
TWO PROOFS OF THE RIEMANN HYPOTHESIS (both published in
The Dartmouth 9/8/0051 9Aug51---that is 1991 in the
unscientific calendar, the scientific calendar starts year
0000 with 1940 the first identification of our Maker.
Discussion: Riemann conjectured that the real component
for the complex numbers at which the zeta function equals
zero is 1/2. This conjecture of Riemann is: the #1, major,
sought-after unsolved problem in all of mathematics.
Sorry Readers: but these two figures (macpaint did not copy
translate, but figure 1 is seen in Jacobs Mathematics a
Human Endeavor. Figure 1: A logarithmic spiral inside
rectangles of whirling squares. The squares and the
rectangles go out to infinity and thus the spiral goes
out to infinity.
Figure 2: Collapsed wavefunction from a logarithmic
spiral into Riemannian space of an ellipse or sphere. And
sorry that exponents and symbol font does not copy translate.
PROOFS: Two proofs of the Riemann Hypothesis follows
as (A) and (B). Proof (A) of the Riemann Hypothesis uses
a reductio ad absurdum argument. Euler proved that a
formula encoding the multiplication of primes was equal
to the zeta function. Euler's formula in complex variable
form is as follows:
(1/(1-(1/(2c))))x(1/(1-(1/(3c))))x(1/(1-(1/(5c))))x
(1/(1-(1/(7c))))x(1/(1-(1/(11c))))x . . . , where c is a
complex variable, c=u+iv. The Riemann zeta function is
as follows: z(c) = 1+(1/(2c))+1+(1/(3c))+1+(1/(4c))+. . . ,
where c is a complex variable, c=u+iv. Euler's formula
involves multiplication of terms and the zeta function
involves addition of terms of a sequence. Suppose the
Riemann Hypothesis is false then there is a 0 such that
z(z)=0 and z not=1/2 +iy, which implies there is another
0 which is not on the 1/2 real line. Which means
another real number other than 1/2 works as an exponent,
resulting in a zero for the zeta function, and a zero
in the Euler formula. Thus, Riemann zeta function
subtract Euler formula must equal zero. This implies
for any other real number exponent, either rational or
irrational numbers, such as for example the rational
exponents: 1/3,1/4,1/5, . . . (Note: any other
exponent y/x , where y and x are Real numbers and
where the Real number of A^(y/x) such that y not=1,
immediately transforms to a number (A^y)^(1/x)), so
that exponents with a 1 in the numerator entail all
of the Real exponents). Then for exponent 1/3 there
has to exist a number M not=0 where (M+M+M) - (MXMXM) = 0.
Then for exponent 1/4 there has to exist a
number M not=0 where (M+M+M+M) -(MXMXMXM)=0, and so on.
Including the infinite number of cases where the x
denominator is irrational are impossible. Only the real
number 1/2 works since 2 not=0, and (2+2) =(2X2), and
so (2+2) - (2X2)= 0. In all of mathematics, 2 is the
only number where its sum equals its product and where
the sum and product is a new number 4. The property of
zero (not a number) does not produce a new number when
added 0+0 or multiplied 0x0. Therefore only real
component of 1/2 works for the zeta function to equal
zero. Q.E.D.
As a check to see if there are any complex numbers
which have the property of (z+z)-(zxz)= 0 where z=x+iy
2(x+iy) - (x+iy)^2 = 0
2x +2iy - (x^2 - y^2 + 2ixy) = 0 gives a real
component 2x- x^2 + y^2 = 0 and an imaginary component
2iy - 2ixy =0 for imaginary component 2iy - 2ixy =0,
implies 2iy(1-x) =0 thus y=0 or x=1
for real component 2x-x^2 + y^2 =0 when y=0 implies
2x-x^2 =0, (2-x)x = 0 thus x=0 or x=2
for x=1 implies 2x-x^2+ y^2 =0, (2-1)+y^2 = 0,
y^2= -1, thus y= + i, substituting x=1 with
y= + i, into z= x+iy gives z=1+ i^2, thus z=0 or z=2.
Therefore, only the numbers 0 and 2 satisfy
(z+z)-(zxz)= 0.
Q.E.D.
Proof (B). A geometrical proof follows: It was proved
that the Riemann hypothesis is equivalent to the
following: the Moebius function mu of x, m(x), and
adding-up the values of m(x) for all n less than or
equal to N giving M(N). That M(N) grows no faster than
a constant multiple k of N^1/2N^e as N goes to infinity
(e is arbitrary but greater than 0). Figure1, by
setting-up a logarithmic spiral in a rectangle of
whirling squares where the squares are the sequences:
1,1,2,3,5,8,13,21,34,55,89, . . . 2,2,4,6,10,16,26, . . .
3,3,6,9,15,24,39, . . . then every number appears in at
least one of these sequences because every number will
start a sequence. Since all numbers are represented
uniquely by prime factors (the unique prime factorization
theorem or called the fundamental theorem of arithmetic)
and The Prime Numbers Theorem: the distribution of
prime numbers is governed by a logarithmic function,
where (N/Logarithm of N).
It is one of the most beautiful things in all of the
known world, that the distribution of prime numbers is
governed by a logarithmic function where these two
mathematical concepts-- one of prime numbers, and the
other, logarithms seem unconnected at first appearance,
but in reality they are totally connected.
Geometrically, the logarithmic spiral exhausts every
positive integer, see figure 1. The area of the
rectangles containing the logarithmic spiral is always
greater, since the spiral is always inside the rectangles.
Thus the Moebius function k N^1/2N^e is satisfied since
the area of the logarithmic spiral is less than the
rectangle whose area represents the number N, and whose
sides represent its factors. The area of a logarithmic
spiral is represented by r=r0e^Ej , and so depending on
where the point of origin for the spiral is taken r0
determines k, and depending on the value of E, E
determines the e value for N, when E=0 then the
curve is a circle. The logarithmic spiral inside
rectangles of whirling squares implies that for any
number N then N^1/2 is the limit of the factors for N,
for example, given the number 28, then 28^1/2=5.2915. .
and so looking for the factors of 28, it is useless
to try beyond 5 because the factors repeat, 4X7 then
repeats as 7X4. But if the Moebius function was false
then there must exist a number M such that M^1/2 is
not the limit of the factors for M and the spiral is
outside of the square, which is impossible, hence the
Moebius function is true. Therefore the Riemann
hypothesis is proved. Q.E.D.
An electron has intrinsic spin of +1/2, only the
positive value of 1/2 works for the spin quantum number
ms, no other number works. Spin quantum number has
positive values only, but spin states for an electron
or proton can correspond to s' = +1/2 and s'' = -1/2.
I assert our observable universe is the last one
electron in the 5f6 of a plutonium atom. Then the zeros
of the zeta function are the charges added-up and so
protons cancel with electrons, no net charge remains,
because matter comes into existence from spontaneous
neutron materialization and thus there can not exist
any net charge since through radioactivities a neutron
transforms into a proton plus electron. Thus the zeta
function is a quantum chart of every neutron, proton,
electron, and atom which came, or will come into
existence. The uncollapsed wave function (figure1) of
quantum mechanics represents numbers of mathematics
such as irrational, transcendental numbers such as e
and pi. The collapsed wave function (figure2) is the
materialization of an atom or subatomic particle,
where materialization substitutes for existence of a
rational number. The number 2 which is 1+1 represents
the Plutonium Atom Totality itself, the next term
represents perhaps the first hydrogen atom to exist,
and so on for every term in the zeta function.
The number 2 is the number for Bohr's complementary
principle where all matter has dual complements of
particle and wave. Matter can not exist without two
things at once, thus 2 is the existor function. The
totality-- one plutonium atom exists in duality with
atom parts and at least one of those atom parts is
itself. There are 4 quantum exclusion numbers
(n, L, mL, ms); 4 uncertainty conjugate variables of
position, momentum, energy, time; 4 interactions (forces)
of physics; and 4 mathematical operators. All of these
because 2X2=2+2=4. Spin of an electron is a dynamical
system, for without spin then change would approach zero.
Thus, the 1 Plutonium Atom Totality divided by the
existor function of 2, gives 1/2 for electron spin.
-------------------
Both of my Riemann Hypothesis proofs are wrong for in the decades of 2000, I would end up correcting Logic of its connectors, and find out that proof by Reductio Ad Absurdum is not a valid proof method of mathematics. And although my above alleged 2 proofs of RH look good cute and sweet, both are Reductio Ad Absurdum. Both are fake proofs.
And not until 2013 when I ventured into calculus and found a geometry proof of Fundamental Theorem of Calculus, did I painfully come to realize that the Riemann Hypothesis was not the important problem of the time, but rather, a geometry proof of calculus was the most urgent problem.
And once I discovered the geometry proof of Calculus I had to go back and throw out all the Numbers of Old Math, which means RH is thrown out and into the trashpile of fake conjectures.
So what was an alleged 2 proofs of Riemann Hypothesis in 1991 turns out to be 2 fake proofs and only by 2011-2013 would the true proof of RH-- a disproof of RH, would emerge.
If I had to write a Aesop fable or parable story of AP and Riemann Hypothesis, the theme is, difficult problems need decades to settle, not years, and only with much much more maturity can one find the correct path. And the correct path is 180 degrees opposite your initial path.
12) The Summary of Riemann Hypothesis and its Disproof.
Sep 19, 2023, 1:30:33 AM
to Plutonium Atom Universe
In the year 1991, after my discovery of the Plutonium Atom Totality in 1990, I assigned myself the task of proving the world's 10 worst outstanding conjectures. In 1991, I was eagerly writing the book on Atom Totality, but wanted some sideshow of math problems. For some reason, my mind gets fidgety if I work on only one problem. My mind is more at ease if I have several irons in the fire, all at once. So as I get stuck on one, my mind shifts to another.
Of course, well, I was a mathematician in training at University and that is what my degree was in, not physics. But the Atom Totality theory was pure physics, revolutionary physics.
I should briefly mention how I come to discover the Atom Totality theory, for all my science gushed forth after the Atom Totality theory.
In early 1970s, after 1972 graduating from University of Cincinnati with a degree in mathematics, and soon to be a teacher in mathematics, I set myself on a personal course challenge, to "mathematize the Darwin theory of evolution". Throughout my life I have given myself personal challenges, much like the one in 1991 to conquer the 10 worst math problems of the time.
Well I never expected to actually solve my first great challenge of mathematizing the Darwin theory of Evolution. What I mean by that is make evolution be like a mathematical formula or a mathematical geometry pattern.
And so, in the years 1972 through 1990, I kept reading books of science that may help, and of course physics books, looking looking for some key idea that could turn biology evolution into a math pattern.
To my amazement, I would achieve my long goal of mathematizing Darwin Evolution. It was a solution far far beyond the scope of my initial problem. I discovered the Atom Totality theory in 1990. I was surprised because I was working on a stock-market-business book and let my science efforts languish.
But sure enough, as I was making notes on physics, and that the Atom was pictured as electron dot cloud, and one night before bedtime looking at the stars overhead, my mind put 2 and 2 together. That the Atom was a Electron-dot-cloud, and the stars and galaxies was a dot-cloud. In my sleep I had come to the realization that the Universe was a single big atom, and the most pressing thing on my mind that morning was to ride my bicycle to the physics library and find out what chemical element fits best the Atom Totality-- it was plutonium to make the special numbers of 137 fine structure constant, pi and 2.71828....
Now the reader is not going to understand how an Atom Totality solves Darwin Evolution as being a math pattern or formula. But as I was writing the book in 1991 and doing math proofs on the side. I realized that the quantum theory of physics had a Superdeterminism in it. The John Bell Inequality where Dr. Bell talks about no free will in the universe. Today some call this quantum entanglement, but prefer Superdeterminism. Superdeterminism takes over on Darwin evolution and makes evolution be a rule rather than a science law or theory. Fate is what drives biological change in the math of quantum mechanics.
Still, surrounded by all these new ideas in 1991, I wanted a new challenge, and I chose to do the worst 10 math unsolved problems, and perhaps the biggest one on that list was the Riemann Hypothesis, RH.
The reason the RH was so big is because so many other problems of math hinged on whether RH was true or not true. Whereas most of the other unsolved problems were of the type that hoo hum, who cares.
So RH was also my most pressing of the 10, I selected. And as the months rolled by, and years rolled by I tackled more problems, so the list grew to 13.
But I solved most of the original list of 10 in the year 1991. However as the years rolled by especially after 1999 working on Logic, I discovered the method of Reductio Ad Absurdum was not a valid math proof method. And I had to go back to all those 10 proofs and see which were reductio method and either fix or admit I had no proof thereof. Sadly my Riemann Hypothesis proofs, I had two proofs of RH were Reductio Ad Absurdum-- proof by contradiction. I had to find a new method and say I had no proof of RH.
But then a fortunate discovery in 2013 as I was doing True Calculus textbook and discovered a geometry proof of the Fundamental Theorem of Calculus, FTC. I instantly recognized it as a proof of FTC, but only later realized it was a proof provided the true numbers of mathematics were Decimal Grid Numbers.
And herein, in 2013, I could go back to my RH proofs and solve them-- mind you, not to prove the conjecture, but the exact opposite, a disproof of the Riemann Hypothesis. RH was a false conjecture. It was not true, for it did not use the true numbers of mathematics.
And that is the reason no-one has ever proved RH. And no-one will, for the Reals and Complex are fake numbers.
When you have a mathematics, and of course you have to have numbers for mathematics. But if your numbers are fake numbers-- Rationals, Irrationals, Reals, Complex, if you have fake numbers. Your mathematics will one day come up with a mighty big conjecture, just as Riemann did in 1859 with the Riemann Hypothesis. And because you math is based upon fake numbers, that conjecture will never have a proof, nor can it ever have a proof because the system of numbers is all wrong and fakery.
So as I found this geometry proof of Fundamental Theorem of Calculus, the true numbers of mathematics need to be discrete numbers and the Decimal Grid Numbers are discrete. I found the world's first valid proof of FTC in 2013, and found that the true numbers of mathematics are discrete Decimal Grid Numbers.
Then, going back to Riemann Hypothesis, only I had no time to revise my proof in 2013. Going back in my mind, I realized when a day came and free of other work, I will write my 1991 RH proof as a Disproof of the Riemann Hypothesis.
So all in all, actually the most important proof AP ever made was the Fundamental Theorem of Calculus, for it completely destroyed RH and set it to right with a disproof.
Was RH a waste of my time in 1991?? Of course not, for I firmly believe the engagement, whether correct or incorrect, the engagement is the most important thing. For if not for the 1991 engagement, I probably would not have a disproof of RH today.
Archimedes Plutonium
Sep 19, 2023, 1:44:55 AM
to Plutonium Atom Universe
I am going to use Wikipedia's Statement of the Riemann Hypothesis ---
--- quoting Wikipedia on RH ---
In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part
1/2. Many consider it to be the most important unsolved problem in pure mathematics. It is of great interest in number theory because it implies results about the distribution of prime numbers. It was proposed by Bernhard Riemann (1859), after whom it is named.
The Riemann hypothesis and some of its generalizations, along with Goldbach's conjecture and the twin prime conjecture, make up Hilbert's eighth problem in David Hilbert's list of twenty-three unsolved problems; it is also one of the Clay Mathematics Institute's Millennium Prize Problems, which offers a million dollars to anyone who solves any of them. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields.
--- end quoting Wikipedia on the statement to be proved of RH ---
I also note that the Clay Mathematics Institute has a reward of money for proofs of those three mentioned. AP proved all three and so the Clay... owes AP at least 3 million dollars, but AP charges interest and so from starting date of this post September 2023, I charge interest on that $3,000,000. For AP is fed up with outfits like Clay, like Beal who offer money as a advertisement stunt and never pay out. These are con-artists stunts. And AP firmly believes that science achievement never needs the hideousness and folly of low life-s making science a money grub game.
Archimedes Plutonium
Sep 19, 2023, 2:34:39 AM
to Plutonium Atom Universe
So in my history of the Riemann Hypothesis disproof, by 2013 I realize the true numbers of mathematics are not the Reals+Complex but that these are fake numbers with their continuum aspect. No calculus can exist in a world of continuums. Calculus needs empty space from one number to the next in order to even have a calculus.
And so, when someone builds a system of science on that of fake elements, it is only a matter of time that someone comes up with a conjecture or hypothesis on that system for which there can never be a proof. Never a proof because the numbers are fakery in the first place.
There is no Riemann Hypothesis when the true numbers of mathematics are Decimal Grid Numbers.
But after 2013, I discovered something else, not as potent as Reals are fake numbers but potent enough. And it goes to show how much the concept of Primes in Old Math had lead many many astray.
For the concept of Primes is a division operation upon Counting Numbers. Numbers in mathematics are well defined, yes Well-Defined, if when doing a operation on two numbers, the result returns you a number that is in the starting given set. Addition and Multiplication are Well defined over Counting Numbers. Hand me any two counting numbers and I add them. They return me another Counting Number. Same goes for Multiplication.
However, hand me any two counting numbers and I divide one into the other. Sometimes they return me a Counting Number but often they do not. 10/5 is a counting number 2, but 5/10 is not a counting number.
Counting Numbers are ill-defined, yes ill defined over division and subtraction. This is why Primes never have a pattern, because they are ill-defined on division. But kooks of math love primes, never figuring out why they have no pattern no formula. They see primes as a mystery to solve, not understanding they are delusional. It is like talking about witches flying on broomsticks in physics class where they laugh you out of the class as a waste of time.
Mathematics wasted its time on Primes, as fake numbers that do not exist. For math is about Pattern, and primes have no pattern, and how could they for they are ill-defined over division. What if I asked you what is the set of bad numbers? Or the set of green numbers? Or the set of sexy numbers? These are more ill-defined sets.
So the motivation of a Riemann Hypothesis and its link to Primes of Old Math caused the RH to be far far over hyped, when in truth, RH was a stupid false conjecture.
Ask yourself in chemistry, is there a concept of primes emerging in the chemical elements? Is lithium element 3 have a quality characteristic of primeness that fluorine element 9 does not have? Or nitrogen 7 compared to phosphorus 15, can we see a primeness in nitrogen but not phosphorus? Ask the same question in physics is there a concept of prime as compared to composite in physics? No, never was.
So prime concept in math became a kook corner for delusional kooks to play around in.
The Riemann Hypothesis was a kook conjecture as a result of the building of mathematics from fake numbers, not the true numbers of mathematics.
Archimedes Plutonium
Sep 19, 2023, 12:33:24 PM
to Plutonium Atom Universe
In my 1991 proofs of Riemann Hypothesis, I used a different statement, the Moebius function equivalent to the RH statement. Funny how Wikipedia entry of the RH talks long, but fails to include the equivalent statement of RH, the Moebius function. In 1991, when I set myself to the task of proving 10 of the worst conjectures in math, one of the very first things I would do, is list any equivalent statement of the conjecture I was trying to prove. To find the one statement that was the best statement for me to start on. Usually I was looking for a geometrical equivalent statement, for my strongest suit in mathematics is geometry, not algebra.
A geometrical proof follows: It was proved
that the Riemann hypothesis is equivalent to the
following: the Moebius function mu of x, m(x), and
adding-up the values of m(x) for all n less than or
equal to N giving M(N). That M(N) grows no faster than
a constant multiple k of N^1/2N^e as N goes to infinity
(e is arbitrary but greater than 0). Figure1, by
setting-up a logarithmic spiral in a rectangle of
whirling squares where the squares are the sequences:
1,1,2,3,5,8,13,21,34,55,89, . . . 2,2,4,6,10,16,26, . . .
3,3,6,9,15,24,39, . . . then every number appears in at
least one of these sequences because every number will
start a sequence. Since all numbers are represented
uniquely by prime factors (the unique prime factorization
theorem or called the fundamental theorem of arithmetic)
and The Prime Numbers Theorem: the distribution of
prime numbers is governed by a logarithmic function,
where (N/Logarithm of N).
It is one of the most beautiful things in all of the
known world, that the distribution of prime numbers is
governed by a logarithmic function where these two
mathematical concepts-- one of prime numbers, and the
other, logarithms seem unconnected at first appearance,
but in reality they are totally connected.
Geometrically, the logarithmic spiral exhausts every
positive integer, see figure 1. The area of the
rectangles containing the logarithmic spiral is always
greater, since the spiral is always inside the rectangles.
Thus the Moebius function k N^1/2N^e is satisfied since
the area of the logarithmic spiral is less than the
rectangle whose area represents the number N, and whose
sides represent its factors. The area of a logarithmic
spiral is represented by r=r0e^Ej , and so depending on
where the point of origin for the spiral is taken r0
determines k, and depending on the value of E, E
determines the e value for N, when E=0 then the
curve is a circle. The logarithmic spiral inside
rectangles of whirling squares implies that for any
number N then N^1/2 is the limit of the factors for N,
for example, given the number 28, then 28^1/2=5.2915. .
and so looking for the factors of 28, it is useless
to try beyond 5 because the factors repeat, 4X7 then
repeats as 7X4. But if the Moebius function was false
then there must exist a number M such that M^1/2 is
not the limit of the factors for M and the spiral is
outside of the square, which is impossible, hence the
Moebius function is true. Therefore the Riemann
hypothesis is proved. Q.E.D.
Comments in 2023, as I read the above some 2023 subtract 1991, some 32 years later, knowing the Primes are a ill-defined notion and realizing that the above was not a proof at all, but a argument in Old Math, using Old Math to its fullest extent. What is missing in the above is the acknowledgement that when you have the false and fake numbers of mathematics-- the Reals and Complex, a jumbled mess of wrong numbers for mathematics. That you end up with a monster of a conjecture that is unprovable, only because the Numbers of Mathematics are never the Reals and Complex.
There is no Riemann Hypothesis idiocy when the true numbers of mathematics are Discrete numbers with empty space in between one number and the successor number.
There is a very astute saying in Ancient Indian and Chinese culture-- do not paint legs on a snake. The RH of Old Math was a snake with legs painted on that snake.
The RH of Old Math was the end extreme of where Old Math could go. They could go to the point where Primes, that horrible ill-defined set of numbers had a pattern as enunciated by the Riemann Hypothesis.
Yet in true reality, Primes are still that obnoxious ill-defined notion with no pattern because division is not a operator on Counting Numbers. Only addition and multiplication are well defined on Counting Numbers.
Can I blame the century of the 20th century of its burning of coal and other fossil fuel for filling the air with lead in leaded gasoline and mercury, to weaken the minds and brains of scientists and especially mathematicians to come up with a Riemann Hypothesis as a patterned primes??? How much can I blame mathematicians for wanted more and more and higher and higher continuity when Planck and quantum mechanics was going in the opposite direction with discrete physics. Yet math with Cohen going 180 degrees opposite with continuum hypothesis.
Can and should we compare the idiocy of the Continuum Hypothesis and the Riemann Hypothesis?
Aha, AP should look into Cohen's silly adventure of continuum. Did Cohen use a Reductio Ad Absurdum for Continuum Hypothesis?? Without looking I would bet 95% that Cohen has a RAA fake proof. Without looking I bet Cohen struck up a RAA argument. And of course RAA is __not a valid___ proof argument.
But back to RH, and it is a miracle, that anyone and everyone neglects the Moebius equivalent of RH. Moebius is a geometrical argument. And why is AP the only one doing a RH proof from the basis of Moebius?
And what is the flaw in AP's above 1991 proof of Riemann Hypothesis?? The only flaw I can see is that it is a Reductio Ad Absurdum RAA argument, and those type of arguments only have a probability of being true, not a valid proof. And that is why I turned to a Disproof argument of RH after the year 2013 when I realized the true numbers of mathematics were Decimal Grid Numbers. There is no RH statement in a world of numbers that is Decimal Grid Numbers, and there are no prime numbers in Decimal Grid Numbers.
The most important proof in the entire 20th century was not RH, but rather was the valid proof of Fundamental Theorem of Calculus. It is a geometry proof for calculus is geometry, and in order to prove FTC, you cannot have Reals and Complex as the numbers of mathematics.
Archimedes Plutonium
Sep 20, 2023, 12:43:30 AM
to Plutonium Atom Universe
Slowly but surely I am revising many of my math books, and about time for much has changed from the 1990s when I discovered the main engine of how they work as a proof, and the succeeding decades. In those succeeding decades I would discover the concept of Infinity needed a borderline to be a precise concept, no longer this loose ended dangling stupid string of "endlessness". The Huygens Tractrix is essential geometry of a figure of endless reach, but finite area, and that is the pivotal concept for a precision definition of infinity-- a borderline. It is a shame that Huygens is not recognized more than what current academics gives him. For Huygens is a towering genius of science, not only math but physics.
So by 2009, I had to go back and look at my proofs done, for the concept of infinity had radically changed, especially my Kepler Packing Problem proof. Then by 2013, another huge change came in that the true numbers of mathematics were not the Reals and Complex with their idiotic continuity, but was the Discrete numbers of Decimal Grid Number Systems, for in Reals, you cannot get a valid proof of Fundamental Theorem of Calculus, but you easily get a valid proof of FTC using Decimal Grid Numbers. Then finally a third major change occurred in 2015 when I finally completed the overhaul of the Logic Connectors, the AND, the OR, the Equal/Not, and the If-->Then. Why is that overhaul so hugely important for math proofs?? It is because Reductio Ad Absurdum, proof by contradiction is not a valid proof method in mathematics. That is worth repeating--- Reductio Ad Absurdum is not a valid proof method in mathematics. It has to do with the truth table of If-->Then connector that a premiss starting out as False cannot conclude a true end result, only a probability conclusion. If the Moon is made of cheese, we cannot get a true conclusion. And this Reductio Ad Absurdum method is the most trafficked, most used method in all of mathematics proof, simply because it is the easiest. And the reason it is the easiest is because it is invalid. Invariably the fake proofs of mathematics in Old Math, invariably over 90% are Reductio Ad Absurdum.
So shortly after 2015, as I overhauled Logic of its truth tables, I realized my Riemann Hypothesis proofs of 1991 and thereafter were invalid proofs because they were Reductio Ad Absurdum. And when I could find some time, I needed to revise RH and other proofs.
Archimedes Plutonium
Sep 20, 2023, 3:04:14 AM
to Plutonium Atom Universe
The Summary of Riemann Hypothesis and its Disproof
Those in Old Math looked upon RH as the big thing, the idol of math proofs. Their big high flying star of math. Turns out that RH was the last symptoms of a dying and dead mathematics. The RH was a conjecture which could never be proved because it used the fake numbers of Reals and Complex in mathematics. And that is very surprizing that everyone in math from year 1900 with Planck and his quantum mechanics and a world of physics of discreteness. Yet here in mathematics, lunatics chasing for more and more continuity with Reals and Complex.
The greatest math problem and challenge from 1800s onwards was not the Riemann Hypothesis in 1859, but was calculus.
Calculus is the highest and greatest achievement of mathematics. And surprizingly from 1800 onwards, no-one in math was inspecting the number one proof of calculus-- the Fundamental Theorem of Calculus, FTC. Oh, yes in the 1800s, Cauchy kept getting penetrating questions from his brightest young students-- who differed with Cauchy on how in the world the integral can go to zero width and still have interior area of the rectangles involved.
Here was Cauchy's great opportunity to make calculus true, by looking for a geometry proof of FTC. No, instead, Cauchy went in opposite direction of cloaking and covering calculus in mud and mire and obfuscation with the dumb "limit analysis". The limit analysis would stop the smart students in his class for Cauchy would end up saying " Young one-- you just do not understand the limit". Limit analysis in math is a stupid silly excuse-- a cover up --- a sham. Each of us, everyday inspect and analyze 10 or more things. I start the day with a quick analysis of what is in the refrigerator to eat on the spot. And Cauchy would think that AP proved something about my refrigerator.
The world of mathematics was knocked off course with the silly RH in 1859 when what was to be done was a geometry proof of FTC. Calculus is the greatest math to date. And we must have Calculus tip top shape as #1 priority.
Instead of the crazy Cohen continuum hypothesis while physics was going 180 degrees opposite in the discrete Quantum Mechanics. Remember-- "quantum" means discrete.
So why were all the mathematicians from 1900 ignoring and sneering at physics in going discrete while they went ever more deeper in a cesspool of continuum?? I lived through math education in college 1968 onwards and I noticed from college and especially books written on math, that mathematicians were arrogant and looked down on physicists. That many in math thought the final thought of the Cosmos would be some math expression. And it is easy to see the hype in the 20th century of E = mc^2 predominated academic circles. So it is easy to see fat-heads among mathematicians, that they were superior elites over physicists. Turns out by 1990 onwards, that the mathematician is the inferior to the physicists. That math is a subset of physics. That physics dominates math. For numbers exist only because Atoms are numerous, and geometry exists only because Atoms have shape and size.
Perhaps the answer to that vexing question of why mathematicians were arrogant and stupid in the 20th century may lie in the environment pollution of the 1900s, where colleges were in big cities and there was tetraethyl-lead in gasoline and there was fossil fuel burning releasing prodigious amounts of mercury into the air, that the brains and minds of mathematicians were laboring under a poisoned brain from lead and mercury. And this makes sense even by 2023, except only with mercury, for many countries banned leaded gasoline. I say that because ask most every math professor of a college or university what is the slant cut of a cylinder and they will say ellipse. Now ask them what is the slant cut of a cone, for a cone is a radically different figure from a cylinder, and the math professor will again say ellipse, when it is truly a Oval for the cone has only one axis of symmetry. Maybe all the lead and mercury they breathed in while in school and thereafter blocks them from seeing geometry truth.
Finally by AP wanting to do a textbook series called True Calculus that omits the limit, that AP stumbles upon a geometry proof of FTC in 2013. In that geometry proof of FTC, it is clear the numbers of mathematics have to be discrete numbers not Reals + Complex. And this destroys Old Math Reals and Complex numbers and destroys their Riemann Hypothesis folly.
RH was folly, not math at all.
AP
zzzzzzzzzz
plutonium dot archimedes at gmail dot com. Looking for a College or University press to hardcover publish all 370+ AP books of science, likely to become 500-600 maybe even 700 books by the time I die. E-books, electronic books are too prone to unbalanced-unhinged censor-editors, who can easily make your books vanish by pulling a switch. Science should never have gatekeepers, who thwart access to true science.
| /
| /
|/______ hardcover or paperback
PAU newsgroup is this.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
Archimedes Plutonium
Archimedes Plutonium
Archimedes Plutonium
Archimedes Plutonium
Disproof of Riemann Hypothesis // Math proof series, book 11
by Archimedes Plutonium
This is AP's 25th published book of science published on Internet, Plutonium-Atom-Universe,
PAU newsgroup is this.
https://groups.google.com/forum/?hl=en#!forum/plutonium-atom-universe
Cover picture: Riemann Hypothesis deals with fake numbers of mathematics. When what is needed is the true numbers-- Decimal Grid Numbers. We learn Decimal Grid Numbers when very young, when just toddlers, wood counting blocks. All the true numbers of mathematics come from Mathematical Induction-- counting. Mathematical Induction is utterly absent in the Riemann Hypothesis, when it should be central to the hypothesis. There never exists a Riemann Hypothesis when the true numbers of mathematics are Decimal Grid Numbers.
--------------------------
Table of Contents
--------------------------
2) My history behind the Riemann Hypothesis disproof.
3) By 2011, I realized the Zeta functions were never equal in the Riemann Hypothesis.
4) True numbers of mathematics are Decimal Grid Numbers, a discovery by me in 2013.
5) True Numbers of mathematics are Decimal Grid Numbers and are discrete, not continuous for they have holes of empty space between one and the next number.
6) Old Math never well-defined Series equality, especially for Euler Zeta and Riemann Zeta.
7) My first disproof of Riemann Hypothesis as seen in 2016.
8) Subtraction Fallacy of Zetas.
9) By late 2023, I found a better explanation of the Subtraction Paradox with years of a calendar.
10) Was the Prime Number Theorem and Fundamental Theorem of Algebra, also fake conjectures and proofs?
11) Is there a Geometry disproof of the Riemann Hypothesis-- yes quite simple and easy!
12) Ongoing commentary and reflection back.
13) The Summary of Riemann Hypothesis and its Disproof.
---------
Text
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1) Introduction and framework of this book.
The Riemann Hypothesis proposed by Bernhard Riemann in 1859 is a conjecture in pure mathematics that the so called Riemann zeta function has its zeros only at the negative even integers and complex numbers with Reals part as being 1/2; was a conjecture never able to be proven and for good reason, for it was the last symptom of a rampant disease inside of mathematics. Old Math did not have the true numbers that compose mathematics. Plus, Old Math never recognized that the Polynomials were the ___only valid functions___ in all of mathematics.
The year 1900 stands out as a magnificent crucial year in the history of both physics and mathematics. That is the year in which Max Planck announced that physics had only discrete numbers and starts the revolution in physics known today as Quantum Mechanics. The word "quantum" means discrete, and opposed to the idea of continuous and continuum. That should have been the year that mathematicians around the world should have examined the numbers of mathematics and questioned why they were so stupid as to plunge further and further into a cesspool sewer of their Reals, negative numbers, complex and imaginary numbers of a ---continuum and continuity--- while physics went the opposite direction--- discreteness is the truth. (See the Cohen nonsense of continuum hypothesis.)
Physicists were smart by year 1900, while the fools and idiots in mathematics never examined anything worthwhile and true, no they plodded along in their stupid Reals and Complex Numbers as numbers of mathematics.
There was a smart mathematician by the name of Leopold Kronecker 1823-1891 who made the remark of "God made the Counting Numbers, all else is the work of man". And what Kronecker was getting at, is the idea that the Counting Numbers, 1,2,3,4,..... are formed from Mathematical Induction. Give me 1 and continue to add 1 gives 2, add 1 to 2 and you get 3, and so forth, all the counting numbers are produced by this constant adding of 1.
Sadly though, it takes until AP after 1990 to show that all the numbers of mathematics can be derived from Mathematical Induction, not just the Counting Numbers. And making "all numbers" crafted by God.
We have to ask the question, was the entire world deplete of logical minds that no-one from Kronecker in 1850 until AP in 1990, could muster the all important question--- If the Counting Numbers are godly numbers because of mathematical-induction, then, could that mathematical induction be applied to all the true numbers that compose and construct mathematics??? Is there a barrier to making all numbers be countable???
AP asked and answered that question by 2013.
Know what Numbers really are, not some sack of crap cobbled together in a junk pile called Reals. Cobbling together Counting Numbers, negative numbers, Rationals, Irrationals and calling them Reals.
History of AP discovery: can be pinned to the year 2013 where Grid Numbers replaces the Reals. I needed discrete numbers not a continuum and by 2013, I started True Calculus, where I need empty space gaps between discrete numbers, in order for calculus to exist. Calculus actually was nonexistent in Old Math because using Reals, you could never prove the Fundamental Theorem of Calculus and that means--- no calculus.
Whenever you have a science, and you see "cobbling together of items"-- means the science is primitive, riddled with error and half-truths, and such was the Reals of Old Math.
10 Decimal Grid is formed with the math induction element being 0.1 and adding 0.1 until we get to 10, the largest number in 10 Grid.
0, .1, .2, .3, .4, . . ., .9, 1.0, 1.1, . . . ., 9.8, 9.9, 10
Next is the 100 Decimal Grid with 0.01 as math induction element shown below.
0, 0.01, 0.02, 0.03, . . ., 0.99, 1.00, 1.01, . . . . . , 99.98, 99.99, 100.00.
Next is the 1000 Decimal Grid system with 0.001 as the math induction element shown below.
0, 0.001, 0.002, 0.003, ..., 0.999, 1.000, 1.001, . . . . . ., 999.998, 999.999, 1000.00
The Grid System all the way up to 1*10^604 as the infinity borderline.
If mathematicians by the time of Riemann had realized the true numbers of mathematics were discrete numbers, all built from Mathematical Induction, there would not have been the stupid Riemann Hypothesis that plagued math for nearly 2 centuries.
Archimedes Plutonium
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Veronika uses a broom to scratch herself, using the coarse brush on her tough hide and the wooden handle on her udder and underbelly.Veronika[a] (born 2012 or 2013) is a pet Braunvieh cow in the Austrian town of Nötsch im Gailtal. She became known in January 2026 after being observed using tools to scratch herself. The incident has been described as the first documented case of cattle using tools, and has led scientists to reassess the intelligence of cows.[1][2][3]
Veronika, a brown cow, was born in 2012 or 2013[1] and lives in the Austrian town of Nötsch im Gailtal,[2] near the Italian border. She is kept as a pet by Witgar Wiegele, a farmer and baker. Veronika started playing with branches that had fallen off trees years before the study was published in 2026,[1][4] and worked out in about 2016[3][5] how to use them as tools to scratch herself, likely driven by a need to alleviate irritation from insects. Wiegele has also reported that Veronika can recognise the voices of her family members and runs over to them when they call for her.[1]