is there a distinction between algebraic irrational and transcendental irrational, or was this a misconception

[Archimedes Plutonium]

Re: explore division getting at the heart of the matter Re: When irrationals are two different rationals acting as one number, means the concept of transcendental is bogus

- show quoted text -
Alright, really great progress here, really great, for I come to realize something that is key crucial to understanding the difference between Rational number and Irrational number. A insight that is able to resolve the question of whether a transcendental irritational exists or is just mumbo-jumbo, that all irrationals come in one flavor== algebraic irrational.

The insight is that roots are not a number, but a process. So that when we say sqrt2 we are not talking about a number but a process of multiplying two numbers to get to 2. Same as sqrt3, which is not a number per se, but a process. When we talk about pi, here again, that is not a number but a process of division, where we divide circumference by diameter. Fortunately, pi is a constant but most processes are variables, and we are not silly to think variable processes are transcendental or algebraic.

Now this insight is key to numbers like A^B where B is irrational, and numbers like .1234567...... (Champernowne's number) thought to be transcendental irrational.

Well, with the insight, we realize there cannot be a distinction within irrationals as to being algebraic or transcendental. They are all just irrationals, one big class, not two subclasses. Irrational numbers are actually not numbers themselves but are processes.

When you divide a circumference (all circumferences are irrational valued distance) by a diameter, they all end up being irrational. And they never can be distinguished as transcendental.

Now because pi never shows up in polynomials, was what started this mess in math, thinking that they are something different than sqrt2. But they are not. In fact pi shows up very often in polynomials, very often, more so than does sqrt2 show up in polynomials.

Every time 3 shows up as 3/1, then, pi has shown up, for 3 is pi in integer Grid. Now what fraction is 3.1 is 31/10, so whenever 31/10 appears in polynomials, we have pi appearing in 10 Grid. Whenever 22/7 shows up in a Polynomial, we have pi showing up as 3.14 in 100 Grid.

So, you see, the entire concept of Transcendental Irrational Numbers was a concept dreamed up by shoddy minds.

Sqrt2 is 1.414 with 1.415 in 1000Grid

Pi is 22/7 in 100 Grid

Both are Algebraic Irrationals, represented by two different Rationals. In Sqrt2, we have 1.414 and 1.415 as a multiplication process. In Pi we have 22 with 7 in division process.

So in both sqrt2 and pi, we need two different Rationals that composes the irrational number.

Thus, the concept of two different classes of irrational was a bogus concept, dreamed up by Logical Impaired minds of math.

AP

[Archimedes Plutonium]

Yes, that is about right. These key ideas, you have to let simmer for a long time before you can see the picture of them. You cannot rush them, they have to simmer on the mind and then, one day they surface and appear in a form of clarity.

What I am talking about is that I want to understand what is a algebraic irrational versus a transcendental irrational and if these transcendentals even exist.

So, no problem with the Algebraic Irrationals. Most all of them are of the form of a root. Say sqrt2 and it is 1.414 along with its complement 1.415 in 1000 Grid, because if you multiply those two different numbers you get exactly 2.000 in 1000 Grid, and never mind if there is digits after the 2.000 that are not zeroes. In Grid Systems, you are exact only to the Grid, and forget about the beyond.

So, this is why Irrationals are so very very much different than Rationals, in that Irrationals are two different numbers acting as one number. if you had a distance length of sqrt 2, starting at 0 and walking along the x-axis to reach sqrt2, what you will find, is that as you reach 1.414, it vibrates back and forth between that and 1.415.

A Rational number is a single solo number, not two different numbers but a single solo number. A Irrational Number is always two different numbers.

So, now that description is of the Algebraic Irrational numbers. But is there another category of irrationals called Transcendental Irrationals where pi and 2.71... are the main major two residents?

Does the concept of Irrational have two categories? Here that idea was simmering for many days now. And I finally realized the answer.

There is only one category of irrational, there is no separate category of Transcendental.

Now I have no proof that Transcendentals do not exist, for the proof of nonexistence is a somewhat mis-logic. How do you prove something does not exist. Perhaps there is a proof and mighty easy proof. It would hinge on the idea that if we define irrational as two different numbers acting as one number and where algebraic irrational exists in polynomials, then you have exhausted the "act routine" with two different numbers. That is, three different numbers or more acting as one are always provided by two different numbers acting as one.

So, we must go back and see the strongest case for having Transcendental and see if we can pick that apart as flawed reasoning. And we go to the pi and 2.71.. argument. Here the argument is that pi and 2.71... never appear in polynomial solutions. But, now, a man of Logic would say, well, of course, Polynomials were never about circles in the first place, so you cannot expect pi to show up when polynomials are barren of geometry circles. But if you had a subject of Trigonometry, good god, pi and 2.71... shows up almost everywhere.

So here we see that the idea of Transcendental concept comes from a skewed and biased and irrelevant arena-- polynomials only. And if we asked the reverse question of having just a circle and the numbers that exist for that circle, since pi is everywhere, that it is difficult to have a point on a circle that is purely Rational, other than say 1, -1, .5, -.5. You are surrounded by irrationals.

So, how do we explain why pi and 2.71... are so different from any root irrational? We explain it by noting that root irrationals are all the multiplication, yes multiply two different numbers. But in pi and 2.71.... it is not clear what two different numbers you multiply. And this is the difference. In that pi and 2.71.... are not multiplication of two different numbers but are the division of two different numbers.

So that in 100 Grid, pi is the division of 22 by 7 which is 3.14 then in 10^4 Grid we have 333/106 = 3.1415

You see, for sqrt of 2 the two different numbers in 1000 Grid are 1.414 with 1.415. For pi as irrational, it is division not multiplication and the two different numbers in 100 grid are 22 and 7, in 10^4 Grid the two different numbers acting as one number are 333 with 106 if we wanted the 10^5 Grid , pi is 355/113. Now 2.71... is the pi analog of a log spiral.

So, in New Math, we solve this problem, by noting that Irrational concept comes in only one type, Algebraic Irrational, and the Transcendental Irrational was as phony as fire breathing dragons or Jack in the beanstalk.

AP

[burs...@gmail.com]

Brain farto nonsense as usual. Whats the dish this
time? Aha grid bla bla pi 22/7 bla bla.

As usual not a sigle line of math, and this already
for 30 years.

[Bill]

burs...@gmail.com wrote:
> Brain farto nonsense as usual. Whats the dish this
> time? Aha grid bla bla pi 22/7 bla bla.
>
> As usual not a sigle line of math, and this already
> for 30 years.

Have you noticed the inverse relationship between mathematical content
and the length of the posts here? It seems "philosophers" will write
and write and write (post, and post and post?), until then "win" the
argument "by exhaustion". : ) Ironically, I think "philosophers" are
above getting their hands dirty with mathematics--maybe they think they
are "too good" for it. At least, that seems true of some of them that
post here. I'm sure there are a vast number of exceptions.

[burs...@gmail.com]

Calling AP a philosopher, is the same as if you
would call a stone, a concert pianist,

AP hasn't produced anything near to being
meaningful math only for one little sentence.

[Archimedes Plutonium]

Newsgroups: sci.physics
Date: Mon, 14 Aug 2017 16:12:42 -0700 (PDT)

Subject: Re: Displacement current replaced by Capacitor current Re:
PreliminaryPage22, 3-7, AP-Maxwell Equations of New Physics/
Atom-Totality-Universe/ textbook 8th ed
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Mon, 14 Aug 2017 23:12:43 +0000

Re: Displacement current replaced by Capacitor current Re: PreliminaryPage22, 3-7, AP-Maxwell Equations of New Physics/ Atom-Totality-Universe/ textbook 8th ed

rockbr...@gmail.com        
5:42 PM (27 minutes ago)


This may also be regarded as a continuation,,,,,,,,,

--------

Hey, Rockbr, thanks, I was hoping someday, someone would post the Maxwell Eq, so I did not have to track down the symbols::



∇⋅B = 0

∇⋅D = ρ

∇×E = - ∂B/∂t

∇×H =  ∂D/∂t + J

[Archimedes Plutonium]

On Monday, August 14, 2017 at 2:27:22 AM UTC-5, Archimedes Plutonium wrote:
> Yes, that is about right. These key ideas, you have to let simmer for a long time before you can see the picture of them. You cannot rush them, they have to simmer on the mind and then, one day they surface and appear in a form of clarity.
>
> What I am talking about is that I want to understand what is a algebraic irrational versus a transcendental irrational and if these transcendentals even exist.
>
> So, no problem with the Algebraic Irrationals. Most all of them are of the form of a root. Say sqrt2 and it is 1.414 along with its complement 1.415 in 1000 Grid, because if you multiply those two different numbers you get exactly 2.000 in 1000 Grid, and never mind if there is digits after the 2.000 that are not zeroes. In Grid Systems, you are exact only to the Grid, and forget about the beyond.
>
> So, this is why Irrationals are so very very much different than Rationals, in that Irrationals are two different numbers acting as one number. if you had a distance length of sqrt 2, starting at 0 and walking along the x-axis to reach sqrt2, what you will find, is that as you reach 1.414, it vibrates back and forth between that and 1.415.
>

So, all Root Irrationals are multiplication of two separate and different Rationals acting as one number.

Sqrt 2 is

1.41 X 1.42 = 2.00 in 100 Grid
then
1.414 X 1.415 = 2.000 in 1000 Grid
then
1.41421 X 1.41422 = 2.00000 in 10^5 Grid

So we see here how Root Irrationals are two different numbers to form a Algebraic Irrational.

But pi and 2.71... are also Algebraic Irrationals, with the only difference from sqrt2 is that the operation is now division, no longer multiplication.

> A Rational number is a single solo number, not two different numbers but a single solo number. A Irrational Number is always two different numbers.
>
> So, now that description is of the Algebraic Irrational numbers. But is there another category of irrationals called Transcendental Irrationals where pi and 2.71... are the main major two residents?
>
> Does the concept of Irrational have two categories? Here that idea was simmering for many days now. And I finally realized the answer.
>
> There is only one category of irrational, there is no separate category of Transcendental.
>
> Now I have no proof that Transcendentals do not exist, for the proof of nonexistence is a somewhat mis-logic. How do you prove something does not exist. Perhaps there is a proof and mighty easy proof. It would hinge on the idea that if we define irrational as two different numbers acting as one number and where algebraic irrational exists in polynomials, then you have exhausted the "act routine" with two different numbers. That is, three different numbers or more acting as one are always provided by two different numbers acting as one.
>

Pi is also a Algebraic Irrational but the operation is division of two different Rationals acting as though they are one number.

22/7 = 3.14 for pi in 100 Grid

then

333/106 = 3.1415 for pi in 10^4 Grid

then

355/113 = 3.141592 for pi in 10^6 Grid

You see how pi is two different numbers of 22 and then 7, then next as 333 with 106

A Rational number is always a single solo number acting as itself, by itself.

An Irrational number is never single never solo, but always with a different partner number. When you have a Rational number length, you have a fixed length, but when you have an irrational length, it vibrates back and forth between to different numbers. At one instant, it is 1.414, then the next time it is 1.415. For pi on a circle, at one instant of time the arclength is 333/106, the next instant it is vibrated to 355/113.

> So, we must go back and see the strongest case for having Transcendental and see if we can pick that apart as flawed reasoning. And we go to the pi and 2.71.. argument. Here the argument is that pi and 2.71... never appear in polynomial solutions. But, now, a man of Logic would say, well, of course, Polynomials were never about circles in the first place, so you cannot expect pi to show up when polynomials are barren of geometry circles. But if you had a subject of Trigonometry, good god, pi and 2.71... shows up almost everywhere.
>
> So here we see that the idea of Transcendental concept comes from a skewed and biased and irrelevant arena-- polynomials only. And if we asked the reverse question of having just a circle and the numbers that exist for that circle, since pi is everywhere, that it is difficult to have a point on a circle that is purely Rational, other than say 1, -1, .5, -.5. You are surrounded by irrationals.
>
> So, how do we explain why pi and 2.71... are so different from any root irrational? We explain it by noting that root irrationals are all the multiplication, yes multiply two different numbers. But in pi and 2.71.... it is not clear what two different numbers you multiply. And this is the difference. In that pi and 2.71.... are not multiplication of two different numbers but are the division of two different numbers.
>
> So that in 100 Grid, pi is the division of 22 by 7 which is 3.14 then in 10^4 Grid we have 333/106 = 3.1415
>

Now what about the irrational 2.71....

It is another division irrational as

19/7 = 2.71 in 100 Grid
then
87/32 = 2.718 in 1000 Grid
then
2721/1001 = 2.71828 in 10^5 Grid

Here again the irrational number 2.71... is not a single solo number but two different Rationals working as one number.

In this light, there are no two different classes of irrationals-- algebraic and transcendental. All irrationals are algebraic, some are multiplication, some division.

> You see, for sqrt of 2 the two different numbers in 1000 Grid are 1.414 with 1.415. For pi as irrational, it is division not multiplication and the two different numbers in 100 grid are 22 and 7, in 10^4 Grid the two different numbers acting as one number are 333 with 106 if we wanted the 10^5 Grid , pi is 355/113. Now 2.71... is the pi analog of a log spiral.
>
> So, in New Math, we solve this problem, by noting that Irrational concept comes in only one type, Algebraic Irrational, and the Transcendental Irrational was as phony as fire breathing dragons or Jack in the beanstalk.
>
>

Now what about Champernowne's number 0.123456.....

It is a division irrational

31/251 = .123 in 1000 Grid
then
309/2503 = .12345 in 10^5 Grid
etc

So, in math, the entire subject field of Transcendental Irrationals was a sham study

AP

[burs...@gmail.com]

Do something useful AP brain farto. Proof that the
Copeland–Erdős constant is transcendental:

0.235711131719232931374143...

I don't see a published proof. If its not
transcendental, it seems so that we could more

or less generate primes from decimal representation
of the root of some polynomial. Since if it is

not transcendental it would be algebraic, and hence
there would be such a polynomial.

[Archimedes Plutonium]

On Tuesday, August 15, 2017 at 12:43:52 AM UTC-5, Archimedes Plutonium wrote:
(snipped)

>
> Now what about the irrational 2.71....
>
> It is another division irrational as
>
> 19/7 = 2.71 in 100 Grid
> then
> 87/32 = 2.718 in 1000 Grid
> then
> 2721/1001 = 2.71828 in 10^5 Grid
>
> Here again the irrational number 2.71... is not a single solo number but two different Rationals working as one number.
>
> In this light, there are no two different classes of irrationals-- algebraic and transcendental. All irrationals are algebraic, some are multiplication, some division.
>

Now, some would say, with their fleeting minds of logic, that the division to make a irrational is reasoning enough to give them their own distinct category as transcendental irrational. That the sequence of 22/7 then 333/106 then 355/113..... for pi and the fractional sequence for 2.71.... is enough of a distinction to warrant two different types of irrationals, the algebraic and the transcendental.

But then, I would counter, that division is multiplication so that we do a 1/7*22, then 1/106*333.

So it is not the multiplication versus division that is driving irrational concept of number. What is driving irrational is the idea that a Rational is a fixed number, a single solo number, yet an irrational is two different numbers acting as if they are one number. And it is that acting that cannot be subdivided into different classifications.

Why is roots irrationals in polynomials but not pi or 2.71....

The reason they are in polynomials, is because those irrationals all have the same pattern of where a chasing of 000s digits is sought for. The sqrt5 is 2.2*2.3 = 5.0 in 10 Grid. So that all root irrationals are the chasing after two different numbers when multiplied gives you a lot of 0 digits. In the case of pi and 2.71.... we do not chase after 0s, no pattern there, but chase after an ever changing digit.

Now, some would interrupt me there and say, well, let us call all Algebraic Irrationals as root irrationals where you chase after 00s digits and define Transcendental irrationals as those irrationals not chasing after 0s digits. What is wrong with that?

Well, let us explore .99999..... and .333333...... for clues

AP

[Archimedes Plutonium]

On Tuesday, August 15, 2017 at 2:26:15 AM UTC-5, burs...@gmail.com wrote:
> Do something useful,,,,,,,,


Jan Burse asks of Andrew Wiles to do something useful for a change.

I have asked Andrew Wiles through the years to do something just truthful for a change like his fakery of Fermat's Last Theorem.

But here Wiles can do something useful and truthful, which Burse can never do for Burse is heading for the asylum, not math.

Wiles can acknowledge that a ellipse is never a conic but that a oval is a conic. The ellipse is reserved for a cylinder section. Can you do that Andrew? Or is life in math always in the fakery lane for you?

[Archimedes Plutonium]

On Tuesday, August 15, 2017 at 5:30:13 PM UTC-5, Archimedes Plutonium wrote:
(snip)

> Now, some would interrupt me there and say, well, let us call all Algebraic Irrationals as root irrationals where you chase after 00s digits and define Transcendental irrationals as those irrationals not chasing after 0s digits. What is wrong with that?
>
> Well, let us explore .99999..... and .333333...... for clues
>

Alright if pi is a progression of divisions of two different Rationals such as 22/7 then 333/106 then 355/113. What is to stop from saying .9999.... and .33333.... are irrationals?

If we say pi is irrational because it is never a single solo number, but two different numbers acting as one number, here for example 22 and then 7, for sqrt2 it was 1.414 with 1.415.

So what is to stop me from saying .99999..... is irrational since it is 9/10 then 99/100 then it is 999/1000.

And here the answer is clear, and why math requires an infinity borderline. Instead of 1*10^604 or its inverse as the true borderline, for sake of simplicity, let us assume 100 was the borderline for ease of writing and of thought.

So, why is 22/7 for pi as 3.14 transcendental while 99/100 for .99 is Rational? Both are a division, both have two different numbers involved, acting as one.

Well, there is one more feature of irrational that I neglected to cover, a Rational ends at the borderline of infinity, going beyond and the number, no matter what, is an infinite number and irrational.

So if the borderline is 10^2 or 10^-2, then .99 is a Rational number and fixed, and is not .99999.... for that is a infinite irrational number. Likewise for .33333.... If the borderline was 100, then .33 is 33/100 and is Rational, fixed solo number.

Now this puts a damper on Old Math's old and ugly argument of whether .99999.... is 1 or is not 1. For if it was 1, as from Old Math's phony argument, then .99999.... being infinite string of 9s and irrational, means the number 1 is irrational, and that is a contradiction.

But more concerning is the fact of .33333.... in Old Math. It is irrational if the 3s digits goes beyond the borderline, but if the 3 digits stops at the borderline or before, those are Rational numbers.

And this makes sense in that in the 100 Grid, the irrational sqrt2 as 1.41 is a Rational number but, 1.414 with 1.415 are two different irrational numbers.

So that easily solves Old Math's eternal silly argument of .99999.... is it or is it not 1, but, it makes the .3333.... now the eternal argument because .333 or .3333 or etc. etc, are all Rationals stopped before the borderline, but, none are equal to 1/3.

In Old Math, 1/3 had to be endless digits of 3, and so 1/3 in Old Math was a irrational number. If it is stopped anywhere along the line, 3/10, 33/100, 333/1000, etc etc before the border it is Rational, but then it is no longer 1/3 for 3/10 is not 1/3. So how is this solved? You see, a far bigger problem than ever was .9999....

Let me continue here,,, later

AP

[Archimedes Plutonium]

Alright, what I am going to need to do here is very exciting, very exciting to me at least me. What I need to do here is pick up on something I started Decades back, ago. Some decade ago, I said, why not have a fraction endpoint on a decimal number.

So that 1/3 as written in decimals is really that of .3333..333_1/3

Now, it is normal for us to write the number 2.3333.... as that of 2+1/3 where we conveniently dispose or carelessly omit the addition sign and write lazily 2 1/3. When we write 2 1/3 we mean 2.3333....

So here, what I am going to do, is say that due to lack of "follow through of logic" we write 2.3333... as 2 1/3

When, if we properly followed Logic rules, we should write 2.3333....333 1/3

In other words, all our troubles with the endless crank talk of .9999.... =1 or the perplexing .3333....

all of that crank talk could have been spared, if we were not so dumb and lazy with omitting the .9999.... of its end tail fraction .9999...999 3*(1/3)

You see, in Old Math, they just forgot that to properly write a decimal that is part fraction, has to be written in and included in the number representation.

So that a number such as .99999.... is a fiction number, just as .3333.... is a fictional number.

When properly written, then .3333.... is .3333...333 1/3 and properly written .99999...999 3*(1/3)

Now, for all the cranks with .9999... =1

Does there crumby argument stand up? No, if falls apart immediately. It crumbles into dust. For, they cannot remove that additional 3*(1/3)

The number .9999..... is a fiction that is poorly written.

Another example of a poorly written number is 1/2 -3. Does that mean 1 divided by 2 then subtract 3 or does it mean 1 divided by -1. So we can write scores and scores of poorly written numbers, that are meaningless because they are obscure, vague, and ill-defined. The same goes for .9999... and .333....

AP

[Archimedes Plutonium]

Now I no longer remember the details of why I invented the suffix, what prompted me, like a prefix, only instead, a suffix, to decimal numbers such as 1/3 written in decimal as .33333...333(1/3). The suffix of 1/3.

I recall the decades ago when I was enamored with p-adics, which may have prompted me to invent the suffix. But once I discovered infinity had to have a borderline, I ditched the p-adics altogether, and saw the p-adics as a waste of time. And with a infinity borderline, the p-adics are a waste of time.

But now, let me focus on this suffix, this proper way of ending a decimal number that continues.

Now a rational like 1/4 is .25000.... and we do not need a suffix, but a rational like 1/3, is not the same as .3333...... and to multiply that representation by 3 to obtain .999999..... is not 1.

Sure, in math, 1/3 times 3 is truly 1. But, .3333.... is not 1/3, but a number ever so slightly smaller than 1/3. So when we multiply .3333.... by 3, we do not get 1, but a number ever so slightly smaller than 1.

Now the reason Old Math found a fakery argument that .99999.... was 1, is that they never logically completed the Representation of a number that is decimal with that of fraction representation.

And it all starts with 1/3.

For all the Counting numbers, 1, then 2, no problems, but now the next number, 3 and to divide with 3 such as 1/3, we run into huge problems of *** did I represent 1/3 ***** correctly when I write it as .33333.....

To people in math and not in math, what I am explaining is that when we go to a bureacracy for drivers licence or whatever, and they represent us by our name. So that my name represents me, exactly, and instead of them putting on a drivers licence Archimedes Plutonium which represents me exactly, they put down Archie Pu. The same mistake went on in mathematics. That the Rational number 1/3 is perfectly sound, true, exacting. But, when math history came around to representing numbers as decimals, a suffix fell through the cracks.

When decimals became widespread, it was just assumed that 1/3 is represented faithfully, fully and truly by .3333333..... and no-one ever thought anything was wrong. But something is terribly wrong for .33333.... is not 1/3. Just as Archie Pu is not Archimedes Plutonium.

What should have happened, but did not happen was that someone should have realized that if you take
1/4 as .25, you get exact answers, but if you take 1/3 as .33, you never get exact answers, and the reason being is the missing suffix.

1/3 is not .3333.....

1/3 is truly .3333..33(1/3)

When you multiply .33333.... by 3 you get .9999.... and that is not 1

When you multiply .33333..33(1/3) by 3 you get .9999..99(1) which is 1.00000....

So, the degenerates of math logic, in the past, wrote up many sham fake proofs, that .9999.... was the same thing as 1. They got away with it, only because they never realized they missed the suffix of decimal numbers. Many Rationals need no suffix for they end in repeating 0s, but for those decimal Rationals that do not repeat in 0s, require a suffix to truly represent the Rational in question.

So when math has some conehead spouting off that .999... is 1, he is a conehead because he has a incomplete understanding of how to fully represent a decimal number, for he misses the suffix.

AP

[Archimedes Plutonium]

Now you talk to people in Old Math about numbers ending in 9s digits such as 1.999.... where they incorrectly claim it is 2.000... and you press them further about those trailing 9s. You often are given the answer as one math professor told me a long time ago is the decimal representation is weak and stressed and flawed with .9999.... =1.

Well today i would reply to that professor that the decimal representation is not weak at .9999.... And what is weak is that those in Old Math never realized they had to add a suffix to every Rational number that did not end in 0 digits.

The Rational 1/9 in Old Math was seen to be .11111....

That is false, totally false.

The number 1/9 is accurately represented by .111...11(1/9) to tell you that 1/9 equals .1111... plus a tiny bit more of (1/9). Sort of like a remainder.

So when we do division of 9 |-------10000 (trying to show long division there) and the student comes up with the answer 1111 and hands it to teacher and is scolded for forgetting the remainder of 1 represented as 1111+1/9 which the teacher wanted to see.

So, in the very same sense New Math needs the remainder in a Rational number represented as decimal if the rational does not repeat in 0 digits.

AP

[Archimedes Plutonium]

On Friday, August 18, 2017 at 1:58:48 AM UTC-5, Archimedes Plutonium wrote:
(snipped)

>
> Now I no longer remember the details of why I invented the suffix, what prompted me, like a prefix, only instead, a suffix, to decimal numbers such as 1/3 written in decimal as .33333...333(1/3). The suffix of 1/3.
>
> I recall the decades ago when I was enamored with p-adics, which may have prompted me to invent the suffix. But once I discovered infinity had to have a borderline, I ditched the p-adics altogether, and saw the p-adics as a waste of time. And with a infinity borderline, the p-adics are a waste of time.
>

I remember the days in which in 1990s we had Deja News and you could easily look up a post you had years earlier. Then along came Google buying out Deja News and searches for older posts became more difficult. I have trouble locating posts of 2009 for this history of subfractions and second decimal point.
Luckily I found this in my own archive.


Newsgroups: sci.math
Date: Fri, 12 Sep 2014 23:52:13 -0700 (PDT)

Subject: introducing SubFractions into math with infinity borderlines #2066
Correcting Math
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Sat, 13 Sep 2014 06:52:13 +0000

introducing SubFractions into math with infinity borderlines #2066 Correcting Math

Now the students would win this argument and show the professor of math his/her failings in a proof
argument. However, the professor has a nice comeback, weak comeback that the students must be prepared to challenge.

On Saturday, September 13, 2014 12:56:12 AM UTC-5, Archimedes Plutonium wrote:
> Alright, here is a test that every math professor would fail in his/her classroom.
>
>
>
> They would put on the board this silly proof argument:
>
>
>
> 3 x 1/3 = 3 x 0.33333.....
>
>
>
> 3 x 1/3 = 1
>
>
>
> 3 x 0.333333..... = 0.99999.....
>
>
>
> hence, 1 = 0.99999......
>
>
>
> Now, how do they fail? They fail because they have no border between what is Finite and what is an Infinite number.  Only with a border between finite and infinite can you ever tell if a number is finite or infinite. We establish that border to be 1*10^603 for large infinity and the inverse for small infinity and establish it because the area of Tractrix equals the associated circle area at that number.
>
>
>
> So, what fake proof has the math professor foisted upon his/her students?
>
>
>
> Well, 3 is finite and 1 is finite according to the math professor involved who has no precision definition of infinity, but their 1/3 as 0.33333.... and their 0.99999.... are infinite numbers by their own admission because those never ending 3s digit and never ending 9s digits is indication that the professor has written an "infinite number".
>
>
>
> So the fakery of their proof is that they end up with
>
>
>
> 1 finite number equals 0.99999..... infinite number
>
>
>
> If the professor was not as lazy as they are, and trace through the Tractrix proof of a border at 1*10^603, then they would realize that
>
>
>
> 1/3 = 0.33333..330000 where there are only 603 digits of 3 rightwards of the decimal point and so the 3 x 1/3 ends up being 0.9999..9900000 with only 603 digits of 9s (corrected) and not equal to 1 but short of 1 by 1*10^-603.
>
>
>
> So, force your math professor to get off his/her laziness and address the key issue of mathematics of our time-- a foolish sick definition of what is finite versus infinite without a borderline. Force them, instead of them brainwashing you.
>
>

Alright, the math professor does have a nice rebuttal by saying, if you have it that way then
how do you ever get

1/3 + 2/3 = 1 for you would have 0.3333..33000.... + 0.6666..660000.... = 0.9999..990000
which is shy of 1 by 1*10^-603

Here the students must challenge the professor yet again by saying

1 divided by 3 as in 1/3 fraction representation is 3 into 10 is 3 with remainder 1 and another 3 into 10 with remainder 1.

So, what is 1/3 fraction representated when Infinity borderline is 1*10^603 and its inverse?

1/3 is then equal to 0.33333..33(1/3)0000.... where you have a sub-fraction inside a decimal. It has no place value in the decimal representation but is a carry over of the 1 in division. The 0 digit rightwards starts at the 604th place value. So to accurately represent 1/3 as a decimal when it hits the infinity borderline, we cannot dispose of the remainder and so a SUBFRACTION occurs.

And 2/3 is then equal to 0.66666..66(2/3)0000.... and when we add the 1/3, and 2/3 the subfractions make up for that 1*10^-603.

I think I introduced subfractions in the last 5 years and this is not the first time I introduced them. I probably called them something different, 5 years ago. The need for them is that fraction and decimal representations alone are not adequate for a mathematics that has a borderline between finite and infinite. When I did Calculus in grid systems, the grids took care of these subfractions.

---- end of old post of 2014 ----

Now in that old post I said that approx 5 years earlier I had discovered or invented this tack on of a decimal with a fraction increment. That would have been 2009 of that invention of the subfraction. And today here in 2017, I need that tack-on ever so much more.

For you see, if math has division of this
__________
9 | 10,000

= 1111 and we must never forget the remainder as +1/9

Then a HUGE, HUGE Error occurred in math history when they thought that

1/9 was .11111111............

You see, they were smart enough to realize that 9 into 10,000 was not 1111 but was 1111+1/9

But, far far too dumb, too stupid to realize that 1/9 is .11111(1/9) and instead thought it to be .11111.....

Likewise the ignorance extended to 1/3 was .3333.... when it really was .3333(1/3) and that .9999..... is not equal to 1, but is a sliver shy of being 1. The number 3 times .3333(1/3) is .9999(3/3) is .9999(1) is equal to 1.

So, it is tricky, it was dicey, for mathematicians, when the decimal representation was introduced into Western Civilization by Fibonacci in 1202 with Liber Abaci (Book of Calculation), whether mathematicians were going to be brilliant in recognizing you needed two decimal points or whether they were going to be failures of logic and have just one decimal point

When we correctly write 1/3 as a decimal we have two decimal points the first being . as in .33333
and the second decimal point is written with a paranthesis such as .33333(1/3)

So the first decimal point is . and the second is (1/3) and it matters not how many 3s you write in

.33333(1/3)
is the same as .33333333333333(1/3)

for the second decimal point (1/3) is at the infinite borderline.

Now, how do we write just the plain .333333......

And that is not 1/3, as you understand by now

To write .33333..... properly is to write .33333(0) which means that at the infinity borderline 1*10^604 (back in 2014 I mistakenly thought it was 10^603) the number .33333(0) has 604 digits of 3 and then the number stops, for no Rational number extends beyond 604 digits, and where only irrationals and infinite numbers are encountered after the borderline.

I am tired of looking and will just place it on faith that it was 2009 that I invented the second decimal point, the added on increment that makes 1/3 not be .33333.... but rather be .33333(1/3).

Today I call it the Suffix for it is a quick easy term and expresses a remainder sort of idea.

Now, why could not the mathematicians from Fibonacci onwards have realized that 1/3 is not really .333333..... and is missing that suffix, that increment, that remainder. Why oh why were mathematicians so very stupid and idiots of the subject? Why? Well, the answer is that math rarely has anyone with a 1/3 brain of logic. Most mathematicians are awarded a college degree in mathematics fueled by a 1/99 brain of logic abilities, for we can see this in the fact that the nattering nutters math professors could not even see that a conic section is never a ellipse, but is an oval.

If you have math professors teaching that a conic section is an ellipse, there is no hope that these fools could ever discover the missing remainder in a decimal representation of 1/3, no hope. You would be lucky a math professor, if male, can count his balls and get the same answer the second time.

AP

AP




AP

[Archimedes Plutonium]

On Friday, August 18, 2017 at 4:20:26 PM UTC-5, Archimedes Plutonium wrote:
> On Friday, August 18, 2017 at 1:58:48 AM UTC-5, Archimedes Plutonium wrote:
> (snipped)
> >
> > Now I no longer remember the details of why I invented the suffix, what prompted me, like a prefix, only instead, a suffix, to decimal numbers such as 1/3 written in decimal as .33333...333(1/3). The suffix of 1/3.
> >
> > I recall the decades ago when I was enamored with p-adics, which may have prompted me to invent the suffix. But once I discovered infinity had to have a borderline, I ditched the p-adics altogether, and saw the p-adics as a waste of time. And with a infinity borderline, the p-adics are a waste of time.
> >

Actually I do not remember if I invented the suffix, the second decimal point before I discovered the infinity borderline or whether I discovered the second decimal point after the borderline discovery.

Well, I do recall infinity border idea was discovered by me in 2009, so 2009 is a very important year of discovery and even invention for the second decimal point was a invention by me starting 2009 in order to resolve the 1/3 dilemma



Newsgroups: sci.math, sci.physics, sci.logic
From: plutonium.archime...@gmail.com
Date: Wed, 21 Jan 2009 18:42:07 -0800 (PST)
Local: Wed, Jan 21 2009 8:42 pm
Subject: #155 Chapter 7, set is infinite only if it contains an infinite number of "infinite specimens", and finite otherwise; new book 2nd edition: New True Mathematics

(snipped in large part)

I believe the largest number in physics is about 10^200 of the Planck
numbers, but
I have to check on that. I worked out in the 1990s that the number of
Coulomb
Interactions that keep a plutonium atom together is of the order of
192! to 231! which
are numbers larger than 10^200. I think 231! is about 10^500.

So what I propose is that since Physics is exhausted of meaning beyond
10^500,
that we peg 0000....0000999...9999 as 10^500 and thus adding 1 more to
that
delivers 0000....0001000....00000

This makes sense for in effect what I have done here is say that
Finiteness is
equivalent to being of Physics Meaning, and beyond that is the realm
of infinity
where we no longer have Physical meaning. Where we can no longer
count, and
so it makes no difference anyway since we can no longer count there.
And that is
what finite means in the first place-- it has a physics reality.
--- end quoting from old 2009 post ---

Now how did I invent the second decimal point? From 2009 to 2014, I was wrestling with 1/3 and its .99999... counterpart. In sci.math, on a daily basis, you could see ignorants debating whether .99999.... was 1 or was not 1, and both sides proffering ignorant arguments.

But in my discovery of infinity borderline, I invented the second decimal point to address problems of numbers like 1/3 as .33333.... once they reached 604 digits (603 back then) of 3s.

---- quoting from text Correcting Math circa 2014 ---
That would make 0 be 999999d999999(1/3+2/3), in 1000 Grid, where the (1/3+2/3) acts as a second decimal point. And where that would be 1000000d000000. So 0 would be a macroinfinity of a higher tier Grid rather than the 10^3 Grid used above.
--- end quote ---

Here you can see that the invention of the suffix, the second decimal point was vital in writing the number zero, 0, as it truly should be written.

Now anyone can search through Google of all my old posts, provided Google is still saving them. Last time I tried with their "Advance Search" I turned up dry.

AP

[burs...@gmail.com]

The golden ratio an irrational and algebraic.
Here have something to play with your paper cutter.
Maybe this is a good training before you move on
to the more complex conic sections. Its a lot of fun:

how to make golden ratio dividers out of paper
https://www.youtube.com/watch?v=ZVWekC10mbY

Its a lot of fun, you can measure things around
your house. Bonus extra exercise, use a compas
and ruler, to construct the ruler, without the
template from cutoutfoldup. Is this possible?

[burs...@gmail.com]

Or promote yourself to an esthetic surgeon:

Phi Brows DIVIDER - INSTRUCTION VIDEO
https://www.youtube.com/watch?v=eeYEYUrDFAI

LoL

[Archimedes Plutonium]

On Friday, August 18, 2017 at 5:17:47 PM UTC-5, Archimedes Plutonium wrote:
> On Friday, August 18, 2017 at 4:20:26 PM UTC-5, Archimedes Plutonium wrote:
> > On Friday, August 18, 2017 at 1:58:48 AM UTC-5, Archimedes Plutonium wrote:
> > (snipped)
> > >
> > > Now I no longer remember the details of why I invented the suffix, what prompted me, like a prefix, only instead, a suffix, to decimal numbers such as 1/3 written in decimal as .33333...333(1/3). The suffix of 1/3.
> > >

It probably was over the case of 1/3. The number 1/3 = .333333.... has bothered me for a very long time, more so than ever did the .99999..... =1. I do recall in College in about 1969 in Freshman Calculus rebuking the idea that .9999.... was 1. So I need not check the dates of anything for that.

But when I started on Usenet in Autumn of 12 August, 1993 the topic of .99999.... was a constant recurring topic. Yet no-one bothered with 1/3 = .3333333.... which to me was far more flawed.

Now, I am worried about dates of discovery, because I want for future readers to see how the Logical Mind in Science works, how the mind arrives at truths of science, the though process. I do not write these dates over bragging rights, I write them to keep the science method of discovery as open to view as possible. It is like teaching people "how to think clearly".

So, with what I can remember of the suffix way back around 2014 and earlier, is that the suffix was used in order for me to describe what the number 0 was. How 0 is an infinite irrational number that comes all the way around the positive rationals, goes into the negative rationals and come home to its resting spot lying in between -1 and 1. Now it was not a complete waste of time for me to do the p-adics, for in doing them, it afforded me landscape views of what infinity was like, and that I could tamper with a second decimal point. Around 2014 or earlier I called the first decimal point as "d".
So that 1/3 was d33333(1/3) with the second decimal point as (1/3)

Now back then I used the dots of ..... to signify gone to infinity.

Do I need those dots now?

Does 1/3 = .333333(1/3) need dots as this .33333...(1/3)

I think perhaps a few dots, say two of them would not hurt. And the two dots signify there are 604 such 3s digits and the (1/3) is the 605th digit.

Now then, the suffix concept was discovered by me sometime in 2009 to 2014 and then lay dormant until its magnificent resurgence a few days ago in 2017 while pondering algebraic and transcendental irrationals.

So the important thing, is that suffix was dormant, and I was looking to understand whether transcendental irrationals are a fake concept and that all irrationals were Algebraic Irrationals. In order to understand that I needed to review what makes .33333.... and .99999.... rational and not irrational. And in this focus and attention on .33333..... I stumbled upon a huge miss, a huge error of Old Math-- that they simply could not write a Rational number as a decimal without including a REMAINDER if the number did not repeat in 0s. That 1/4 is .25 and is exact, but that 1/3 is not .33, because it is not exact and is missing a Remainder. So if we had
_________
3 | 10,000 = 3333 we would be in error, because we forgot the remainder of +1/3 so the answer is

3333+1/3

Same thing goes for 1/3 itself since it is
__________
3 | 1.0000 = .3333 we are again in error unless we include a suffix, a second decimal point of (1/3).

It is this suffix that every mathematician since 1202 with Fibonacci, had missed, in writing a number as a decimal.

We easily understand that 3 into 10,000 has a remainder 1/3, but hard pressed to ever see that the 1/3 LOGICALLY, also needs the remainder.

For 1/3 is never equal to .33333.... but, is equal to .3333..(1/3)

And what that second decimal does, is ruin all those crackpot mathematicians who thought .9999... was 1. That suffix spoils and ruins their argument. Blows it to smithereens.

> > > I recall the decades ago when I was enamored with p-adics, which may have prompted me to invent the suffix. But once I discovered infinity had to have a borderline, I ditched the p-adics altogether, and saw the p-adics as a waste of time. And with a infinity borderline, the p-adics are a waste of time.
> > >
>
> Actually I do not remember if I invented the suffix, the second decimal point before I discovered the infinity borderline or whether I discovered the second decimal point after the borderline discovery.
>
> Well, I do recall infinity border idea was discovered by me in 2009, so 2009 is a very important year of discovery and even invention for the second decimal point was a invention by me starting 2009 in order to resolve the 1/3 dilemma
>

For me, ever since I started on Usenet in August 1993, for me the larger worry was how in the world is 1/3 = .33333..... for whenever you take a snippet of the 3s such as .3 or .33 or .333 etc, you never get the exact answer but always a tad short of any exact answer. Only when you do fractions of say 1/3 times 2+9/16 will you come out with exact answers. So to me, the worry was not about .9999.... but rather, the conundrum of .33333.... And, I knew something that the others seemed not to ever realize, is that .99999.... was a problem that arose out of .33333...., so that if you can solve .3333..... you solve .99999....

>
>
> Newsgroups: sci.math, sci.physics, sci.logic
> From: plutonium.archime...@gmail.com
> Date: Wed, 21 Jan 2009 18:42:07 -0800 (PST)
> Local: Wed, Jan 21 2009 8:42 pm
> Subject: #155 Chapter 7, set is infinite only if it contains an infinite number of "infinite specimens", and finite otherwise; new book 2nd edition: New True Mathematics
>
> (snipped in large part)
>
> I believe the largest number in physics is about 10^200 of the Planck
> numbers, but
> I have to check on that. I worked out in the 1990s that the number of
> Coulomb
> Interactions that keep a plutonium atom together is of the order of
> 192! to 231! which
> are numbers larger than 10^200. I think 231! is about 10^500.
>
> So what I propose is that since Physics is exhausted of meaning beyond
> 10^500,
> that we peg 0000....0000999...9999 as 10^500 and thus adding 1 more to
> that
> delivers 0000....0001000....00000
>

That is history, but what I want to focus on is how I got from suffix to the idea that Decimal Representation is missing a suffix, and how I discovered that.

> This makes sense for in effect what I have done here is say that
> Finiteness is
> equivalent to being of Physics Meaning, and beyond that is the realm
> of infinity
> where we no longer have Physical meaning. Where we can no longer
> count, and
> so it makes no difference anyway since we can no longer count there.
> And that is
> what finite means in the first place-- it has a physics reality.
> --- end quoting from old 2009 post ---
>
> Now how did I invent the second decimal point? From 2009 to 2014, I was wrestling with 1/3 and its .99999... counterpart. In sci.math, on a daily basis, you could see ignorants debating whether .99999.... was 1 or was not 1, and both sides proffering ignorant arguments.
>

Surprizingly the suffix comes up again in recent days in order to help understand the irrational number better, and it is then, that I realized a huge missing piece of the Decimal Representation.

Realizing it only after noting that since
________
3 | 10,000 = 3333+1/3 required a remainder place value in the answer

and likewise
3 | 1.0000 = .3333(1/3) required a remainder place value

> But in my discovery of infinity borderline, I invented the second decimal point to address problems of numbers like 1/3 as .33333.... once they reached 604 digits (603 back then) of 3s.
>
> ---- quoting from text Correcting Math circa 2014 ---
> That would make 0 be 999999d999999(1/3+2/3), in 1000 Grid, where the (1/3+2/3) acts as a second decimal point. And where that would be 1000000d000000. So 0 would be a macroinfinity of a higher tier Grid rather than the 10^3 Grid used above.
> --- end quote ---
>
> Here you can see that the invention of the suffix, the second decimal point was vital in writing the number zero, 0, as it truly should be written.
>
> Now anyone can search through Google of all my old posts, provided Google is still saving them. Last time I tried with their "Advance Search" I turned up dry.
>
>

So, this time around on suffix, I had a power of force of argument, that since
________
3 | 10,000 = 3333+1/3 required a remainder place value in the answer

that
_________
3 | 1.0000 = .3333(1/3) required a second decimal point to compensate for the remainder

So, I discovered suffix and second decimal point back circa 2009, but not until a few days ago in 2017
would I realize that all of mathematics had a incomplete decimal representation of numbers.

If a Rational ends in repeating 0s digits such as 1/2, 1/4, 1/8, etc the end in repeating 0s, then to represent those fractions that do not end in 0s, there must be a suffix, for the remainder.

AP

[burs...@gmail.com]

AP brain farto, producing spam and nonsense
already since 12 August, 1993. Not a single

line of clear thinking. Totally ignorant of
anything math, only crank drivel.

[Archimedes Plutonium]

So now let us try out the oft repeated fantasy of 1 = .9999.... that Old Math adored loved cherished and nurtured as if it was a slice of Paradise, better than a all expense payed vacation.

Their argument was 1/3 = .33333....
But already that was a false claim (similar to the Dandelin fake proof of conics that starts out by saying the cut is ellipse when in fact it is a oval).

Anyway the fakery proceeds by multiplying both sides by 3 to yield 1 = .99999.... And presto, a fake is borne

But now let us see what happens when 1/3 is truly used

1/3 = .3333..33(1/3) with its remainder of +1/3

Much like
_______
3 | 10,000 = 3333+(1/3) and not 3333 missing a remainder

So we multiply .3333..33(1/3) by 3 and get .9999..99(3)(1/3)
which is .9999..99(+1) = 1.0000..000

And this algebra is further confirmed by

2/3 = .6666..66(2/3) when added with
1/3 = .3333..33(1/3) gives 1.0000..000

So, math cannot have both true that 1 = .9999.... And 1 = .9999..99(3*1/3)

Math cannot have 3333+(1/3) equal to 3333

Another example of this is 2/9 is equal to .2222..22(2/9) and not .222222.... For if we take 8/9 = .8888..88(8/9) we come out with the correct answer of 1.1111..11(1/9)
Whereas Old Math comes out with 1.1111..110

AP

[Archimedes Plutonium]

Now the utter beauty in all of this for the question of irrationals is that an irrational can only be algebraic and is easily identified from a rational as having no suffix.

For example Champernownes number .1234567891011... Can have no suffix nor can phi, pi, 2.71... Nor can root irrationals.

But how does the suffix eliminate the transcendental category?

It does so by making the division be multiplication so that in the case of pi 22/7 is 22 x 1/7, two different rationals acting as one number while sqrt2 was 1.414 x 1.415 acting as one number.

AP

[burs...@gmail.com]

Probably APs down syndrom, preventing him seeing
anything math. Conic sections, ovals, yikes!

Only non-transcendental numbers in the interval
[1.4142,1.4143], yikes! Guess what AP, there

are countable many algebraic numbers in the
interval, uncountable many transcental numbers in

the interval. Most of real numbers are transcental:

Lebesgue measure of transcendental numbers in [0,1]
https://math.stackexchange.com/a/887605/4414

[burs...@gmail.com]

Sandeep Silwal:
"If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy."

AP Brain Farto:
"I feel confused, I do mathematics to get even more confused. If am
confused I spam sci.math with my nonsense."

[burs...@gmail.com]

Maybe a property of wonky numbers, those only
definable within 10^604 infinity border, that

by APs mongo math, we have non-transcendentals
in the [1.4142,1.4143] interval. Thats probably

the reason why the conic section is not only
oval, but in fact a rectangle. Here asking

the right questions: Where are the transcendental numbers?
https://math.stackexchange.com/questions/1694302/where-are-the-transcendental-numbers

[Markus Klyver]

Still, I have yet not gotten any sensible answer to why 0 would be irrational or why numbers "beyond the borderline" are infinite.

[burs...@gmail.com]

Well I guess in AP brain fartos world the infinity
borderline is looping back to 0, otherwise symmetry

would be broken, now we have always S(x) exists,
with S(oo) = 0. What is symmetry breaking?

Here Cousin of Ross Finlayson presents the basics:

Noether's Theorem and the Motion of Creation
https://www.youtube.com/watch?v=V-1Oahw7-Zg

[zelos...@outlook.com]

Yes there is a differens for p\in R[x] we have that p(z)=0 for z/in R implies that z is an algebraic number, but for z\in R, if there exists NO p\in R[x] such that p(z)=0, then z is trancendental. It can be shown that these properties are complementary and mutualyl exclusive. So they are a thing you dumnut.