AP's 19th published book -- Proof of the Collatz Conjecture by AP in 2016. Add on a new chapter.

I saw a post in sci.math recently concerning the Collatz conjecture, only the author refused to admit AP had proven it in 2016.

But since 2016, I much forgot the reasoning and rationale of why my proof worked so well. Maybe my age of 72 is wearing on me. Maybe I have so so much science work that I can no longer keep track of it all. And so from the fact that I could not instantly remember how the proof of mine went. I have decided to add this additional clarity to the published proof.

The clarity that 4 Consecutive Even numbers must have at least one of the four divisible by 8. When we have one of the four consecutive evens divisible by 8 and are Mandatory to select that even number, we slide down close to 1 by a factor of 8, while the odd number raises us upward by no more than a factor of 3 in 3n+1. I had forgotten that it is Mandatory to chose and pick the Even number out of 3n-3, 3n-1,3n+1, and 3n+3.

Old Math Collatz is unprovable unless and until it sharpens its Statement.

Whenever a number is selected, whether odd or even. If Even, then you divide by 2 until you come to a odd. If we land on a Odd number you must review 3n-3, 3n-1,3n+1, and 3n+3. Once you have those 4 consecutive Evens, you must pick the one which is at least minimum divisible by 8. And hence you slide down at least by 8 times whereas you rise by no more than 3 times. Hence the proof for you always converge to 1.

Now the world is full of assinine people who will try to prevent AP from getting credit for proving Collatz, they attack you anyway possible to deny you credit. And the usual attack of AP's proof is that I altered the Statement so much that it is no longer Collatz. Not true. For the original Collatz is "indeterminate in proof". No-one can prove the original Collatz for it is a statement of "fog". I can dream up millions of math statements that looks like a "well formed math statement" but is actually fog. For instance, the No Odd Perfect Number Statement, when you place the definition of factors in a fog. Is 9 in No Odd Perfect Number, is 9 to be 1+3 or is it to be 1+3+3 for that 6 in Even Perfects is 1+2+3. And so why are idiot mathematicians with no logical brains forcing 9 to be 1+3 when it should be 1+3+3 to follow the same logical rules as 6 is 1+2+3. Same for Collatz, you have mathematicians with no logical brains saying that if you land on a Odd Number, you must only consider 3n+1, with no link or connection to the surrounding even numbers of 3n+1. A fog conjecture that can never be proven one way or another unless the idiot mathematician goes through ever entire integer from 1 to that of 1*10^604, which no computer can ever do for that is longer than the age of the Universe.

Here is another fog statement which looks like math only it is foggy and indeterminate. Prime numbers can be placed in a string of any length you want and separated by a Even number. Here is a string of 3 primes separated by distance 2-- 3, 5, 7. That appears to be a valid well defined statement of mathematics. But it is not. It is fog and indeterminate. It is fog because primes never existed in the first place for Counting Numbers are not well defined on division. To be well defined, means that every counting number A, B in A/B returns another counting number. Counting Numbers are well defined on addition and multiplication, but division no. Same as Subtraction is not defined well on Counting Numbers.

The reason that Mathematics has no pattern for Primes with a single formula that encompasses all Primes, is the reason that Primes are not defined for division.

The true numbers of mathematics are Decimal Grid Numbers and in them-- there does not exist a concept of "prime". Primes in mathematics are as goofball fakery as to think that we have Santa Claus in physics classroom.

Here is another example of what appears like being math statement but is in fact fog. The sine function of Old Math forms a sinusoid curve, so says every Old Math textbook taught in High School. Yet if we had a logical brain which is few and rare in modern times. We understand the sine function as being the opposite / hypotenuse of a right triangle that goes around a unit circle. That means the unit circle makes the hypotenuse be 1 in length. That means the right triangle for sine function follows the exact same track as the path of a unit circle. That means the graph of the sine function is never a sinusoid but a semicircle graph.

Almost every conjecture in Old Math that was unproven, needed first, a doctoring up of its initial Statement. The statement was deeply flawed and never allowed a proof.

I stated all of that in my book and even on Usenet sci.math by 2016. But all of us in science are required to constantly update and make more and more clear as to what we discovered. So in that light I will add a new chapter of a 2022 review of my 2016 proof of Collatz.

19th published book

World's First Proof of Collatz Conjecture// Math proof series, book 6 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 20Aug2021. This is AP's 19th published book.

Preface: Old Math's Collatz conjecture, 1937, was this: If you land on an even number, you divide by 2 until you come to an odd number. If you come to or land on an odd number, you do a 3N+1 then proceed further. The conjecture then says that no matter what number you start with, it ends up being 1..

What the Collatz proof of math tells us, is that so very often mathematicians pose a conjecture in which their initial formulation of the conjecture is murky, obfuscation and poorly designed statement. Such poorly designed statements can never be proven true or false. An example that comes to mind of another poorly designed conjecture is the No Odd Perfect Conjecture, in which the statement is obfuscation of factors. So for the odd number 9, is it 1+3, or is it 1+ 3 + 3. So when a mathematics conjecture is full of obfuscation and error in the statement, then these type of conjectures never have a proof. And takes a person with a logical mind to fix and straighten out the conjecture statement and then provide a proof, thereof.

Cover picture: when I think of Collatz, I think of a slide, a slide down and so my French curve is the best slide I can think of, other than a slide-ruler, but a slide ruler is slide across.

Product details
• ASIN ‏ : ‎ B07PS98K5H
• Publication date ‏ : ‎ March 16, 2019
• Language ‏ : ‎ English
• File size ‏ : ‎ 1955 KB
• Text-to-Speech ‏ : ‎ Enabled
• Screen Reader ‏ : ‎ Supported
• Enhanced typesetting ‏ : ‎ Enabled
• X-Ray ‏ : ‎ Not Enabled
• Word Wise ‏ : ‎ Not Enabled
• Print length ‏ : ‎ 61 pages
• Lending ‏ : ‎ Enabled
• Best Sellers Rank: #212,131 in Kindle Store (See Top 100 in Kindle Store)
◦ #4 in 45-Minute Science & Math Short Reads
◦ #9 in Number Theory (Kindle Store)
◦ #32 in Number Theory (Books)

Yes, I need to write a new chapter as a 2022, clarification on my 2016 proof of Collatz. When I cannot remember the mechanism of the proof, some 6 years later, means I need to add more clarity.

Dan Joyce being opaque about the Collatz conjecture. Probably because Dan does not want to give credit to AP for proving Collatz in 2016.

Dan Joyce being opaque about the Collatz conjecture. Probably because Dan does not want to give credit to AP for proving Collatz in 2016.
On Monday, May 30, 2022 at 4:02:28 PM UTC-5, Dan joyce wrote:
> Simplifying the 3n+1 problem where any starting odd number will always

Here is AP's proof of Collatz--
World's First Proof of Collatz Conjecture// Math proof series, book 6 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 20Aug2021. This is AP's 19th published book.

Preface: Old Math's Collatz conjecture, 1937, was this: If you land on an even number, you divide by 2 until you come to an odd number. If you come to or land on an odd number, you do a 3N+1 then proceed further. The conjecture then says that no matter what number you start with, it ends up being 1.

What the Collatz proof of math tells us, is that so very often mathematicians pose a conjecture in which their initial formulation of the conjecture is murky, obfuscation and poorly designed statement. Such poorly designed statements can never be proven true or false. An example that comes to mind of another poorly designed conjecture is the No Odd Perfect Conjecture, in which the statement is obfuscation of factors. So for the odd number 9, is it 1+3, or is it 1+ 3 + 3. So when a mathematics conjecture is full of obfuscation and error in the statement, then these type of conjectures never have a proof. And takes a person with a logical mind to fix and straighten out the conjecture statement and then provide a proof, thereof.

Cover picture: when I think of Collatz, I think of a slide, a slide down and so my French curve is the best slide I can think of, other than a slide-ruler, but a slide ruler is slide across.

--------------------------
Table of Contents
--------------------------

Part I: AP researches the Collatz conjecture in 2016 and proves it with 4 Consecutive Evens.

Alright tonight I dozed off for about an hour and once awoken I had Collatz proof of mine on my mind. Trouble was I could not remember the structure of my proof so had to review what my 2016 proof was.

It is very well and nicely contained. It is a very strong proof.

What it says is this-- quoting from my book.

Proof at last Re: 3/8 increments of fall in Collatz Re: Mechanism shown for 75, as to why Collatz works; preliminary Full Collatz 3N+-1 simultaneously 3N+-1 proof; disproof of half-baked Collatz 3N+1
Mechanism shown for 75, as to why Collatz works; preliminary Full Collatz 3N+-1 simultaneously 3N+-1 proof; disproof of half-baked Collatz 3N+1

Alright, what that mechanism means is given any odd number, say we are given 75, then the even numbers surrounding 75 from 3N-3, 3N-1, 3N+1, 3N+3 will always have a even number that has three divisions by 2. So for 75 the 3N is 225. And thus we have a choice 3N-3=222, or 3N-1=224 or 3N+1=226, or 3N+3 =228. One of those choices has at least three divisions by 2 and perhaps one has more than two. So, let us see. 222=2*111, 224=2*2*2*2*2*7, 226=2*113, 228=2*2*57.

So here we have the even number 224 which has a 2 as factor for 5 times.

So Old Math can prove that in any given odd number larger than 1, that we always have a three factor of 2 even number produced. So that Collatz mechanism is that we multiply by 3 any odd number, but we end up by dividing by at least 8 any even number produced, because one of those even numbers is always divisible by 8.

--- end quote ---

So what the proof basically is-- is given any 4 consecutive even numbers such as the example of 222, 224, 226, 228 that one of them is factorable --at minimum-- by 8 and thus has a reduction of at least 8 times. In my case example 224 is factorable by 2 for 5 times, mind you not 10 but 2*2*2*2*2 = 32.

And what solves the proof is that we alter the statement of Collatz to mean that we Have A Choice of Even Number. We have a choice of picking 3N-3, 3N-1, 3N+1, or 3N+3 which 222, 224, 226, 228 are a result of the odd number 75.

So the Proving Mechanism is this choice of 4 even numbers and we must pick, yes, must select the highest factorable even number of those four numbers. That means in each Collatz up tick from a odd number is no more than 3 times but every even number will be a down slide by a factor of at minimum of 8 times. So, in the proof of Collatz, every number will head for 1, because upward tick is 3 times, but every downward slide is 8 times downward.

This is a feature of math proofs, we tend to forget them as the years pass and need to constantly review how the proof worked.

Now many insane babbling critics will say I altered the statement of Collatz. Yes, I altered a fog statement by illogical degenerates in mathematics to a statement that bears the mechanism of Collatz. There can never exist a proof of Old Original Collatz, for it is a cloudy mess of why the slide occurs. The slide occurs from the structure of even numbers. The smallest set of even numbers is 2, 4, 6, 8 and it is the 8 that is divisible by 2 in four times. It is the mandatory picking of the largest even number in the 4 consecutive evens that proves Collatz.

For the fools that say AP proved something different from Collatz. No, AP only showed that Old Collatz was not a intelligent statement. And I can dream up millions of statements that may look like some math statement but is just a garbled mess, never provable.

AP

Now it maybe the case that the original Old Math Collatz Conjecture of taking only 3N+1 for a odd number landing and not the AP restatement of taking the 3N+-1 and 3N+-3 and checking out 4 Consecutive Evens and forced to pick the one divisible by 8, proving a convergence to 1. It maybe the case that all Counting Numbers from 1 to 1*10^604 behave so that 3N+1 landing delivers a convergence to 1.

But here is the problem, no computer now or ever is going to be able to check all the counting numbers from 1 to 1*10^604 to see if Collatz original 3N+1 is supported. No computer can check that. Hence the original Collatz is indeterminate as a proof. If we added onto Collatz original that all numbers from 1 to 10^6 obeys Collatz 3N+1, then a computer can verify and that limited conjecture is proven true.

In the face of that fog of original Collatz, for we have not even mentioned the "spin potential" where in my published proof I show that a spin endlessly around and around on some number. As I wrote in my proof of 2016.
--- quoting proof ---
Seeing the structure of 5N+5 and wondering how that can have internal spinning around in a trap and how it can diverge to infinity, and wondering why 3N+3 avoids all of that.

Alright, I should discuss this type of Collatz for it shows us how a Collatz can have a "spinning around inside trapped in a spin". Such as 9 with 5N+5

9;;9, 50, 25, 130, 65, 330, 165, 830, 415, 2080, 1040, 520, 260, 130, 65, and spinning around endlessly.
--- end quoting proof ---

So if we go far enough out there such as in the numbers of 600 digits of odd numbers, and with only a 3N+1, can we perhaps run into a spinning around endlessly odd number such as we see for 5N+5.

AP

🧛🏻‍♂️ of Math and 👻 of Physics Archimedes "math hater" Plutonium
<plutonium.archimedes@gmail.com> tarded:

> Yes, I need to write a new chapter as a 2022, clarification on my 2016 proof of Collatz. When I cannot remember the mechanism of the proof, some 6 years later, means I need to add more clarity.
>
> Dan Joyce being opaque about the Collatz conjecture. Probably because Dan does not want to give credit to AP for proving Collatz in 2016.

AP gets no credit for proving the Collatz conjecture in 2016 because AP
never proved the Collatz conjecture in 2016.

If you want credit for proving something, you had better actually prove it!

> Now many insane babbling critics will say I altered the statement of Collatz.

Of course you altered the Collatz conjecture. By having a set of 4
numbers and selecting the one that is divisible by 8, it is no longer
the Collatz conjecture. Since you invented this new conjecture, why not
name it for yourself, say the Plutonium Conjecture or the Arky
Conjecture. It is not the Collatz conjecture because that is completely
different.

> Yes, I altered a fog statement by illogical degenerates in mathematics to a statement that bears the mechanism of Collatz.

No, you altered a statement and made it an entirely different problem.
Call it just about anything you want, except the Collatz conjecture.

> There can never exist a proof of Old Original Collatz,

That's how it is interesting, it is unknown if there is a proof or
disproof of the Collatz conjecture possible.

> for it is a cloudy mess of why the slide occurs.

No, it is perfectly clear. Multiply by 3 and add 1 if odd, divide by 2
if even. Period.

> The slide occurs from the structure of even numbers. The smallest set of even numbers is 2, 4, 6, 8 and it is the 8 that is divisible by 2 in four times. It is the mandatory picking of the largest even number in the 4 consecutive evens that proves Collatz.

No, it is not part of Collatz. Maybe part of the Arky conjecture, or
whatever you want to call YOUR conjecture, but the Collatz conjecture is
not that.
>
> For the fools that say AP proved something different from Collatz. No, AP only showed that Old Collatz was not a intelligent statement.

It is perfectly intelligent. The rules are perfectly clear and intelligent.

> And I can dream up millions of statements that may look like some math statement but is just a garbled mess, never provable.

Like most of your "proofs"!!

Pope Francis, "not one single marble of commonsense in my entire brain" says Kibo Parry M. when AP is arguing that the Catholic Church needs to reform its science in all Catholic Schools. Time is up to remove Creationism from science class and teach Darwin Evolution.

On Wednesday, June 1, 2022 at 10:21:35 PM UTC-5, Michael Moroney wrote:
> "math hater"
> tarded:
> "not one single marble of commonsense in my entire brain"

Roberts, Alito, Kavanaugh, Barrett, Gorsuch, Pope Francis ever examine the education system in Catholic schools and Universities as to how much they are Anti-science, especially biology, especially physics, and whether the "i sick i cry" spamming machine of sci.physics and of Biology science by Catholic church and various fake names is a Catholic Church funded spam organization parked in sci.physics for the purpose of preservation of anti-science taught in Catholic schools.

Hi "i sick i cry spammer", time is running short for the Roberts Court is due to overturn Roe v. Wade in June.

Just look at the Nobel prize record where in Peace 1/2 are catholic while about 1/2 are protestant but in science you need go back to Eccles to 1963 to see a Nobel in science. Clearly, the Catholic Church Education system, along with its "sex abuse" needs huge fixing. And what is there response? They supply spammers of disinformation like "i sick i cry" and his clown act.

Catholic Church, --- why not fix the problems instead of sending in spam machines.

I know the Catholic church needs to clean house of its sex abuse. But they also need to clean house of their Anti-science stance and their extreme hatred of biology-- Darwin evolution. And their silly ideas of abortion, no abortion, when biology has abortion as a normal everyday natural law of biology.

Abortion is a Natural Law of Biology. And woe to any church that thinks they can overturn Laws of Nature.

We see the silly Roberts Supreme Court packed 7 of 9 justices as Catholics, catholics that never learned true science-- truth of the world about to saddle and strap 300 million Americans with "no abortions" regardless that we have a Zika virus epidemic and a Covid virus pandemic. We even see idiots of science of judges meddling into face masks.

So, let us question is the "i sick i cry spammer" is a Catholic Church run and paid for organization to show how bad the Catholic church science is in "physics and biology".

AP

Michael Moroney wrote:

>> Dan Joyce being opaque about the Collatz conjecture. Probably because
>> Dan does not want to give credit to AP for proving Collatz in 2016.
>
> AP gets no credit for proving the Collatz conjecture in 2016 because AP
> never proved the Collatz conjecture in 2016. If you want credit for
> proving something, you had better actually prove it!

agree, but you have to be the first to get that credit. Proving it as
number two earns no credit. Please be careful where you spread your
credits.