What would a Fundamental Theorem of Algebra be like if no negative numbers are allowed

[Archimedes Plutonium]

Newsgroups: sci.math
Date: Sun, 18 Jun 2017 22:23:11 -0700 (PDT)

Subject: we ignore A/0, why not ignore all negative numbers Re: may have found
how to get rid of negative numbers
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Mon, 19 Jun 2017 05:23:11 +0000


we ignore A/0, why not ignore all negative numbers Re: may have found how to get rid of negative numbers

- show quoted text -
Yes, excellent point from a idealist.

Is there negative money? Is there a negative gold coin. Is there a negative paper note to pay for -$1,112.

So what Chris is stumbling over and stumbling upon is his bad case of being brainwashed early in life and now fully accepts the brainwash, and wants to pass that brainwash off on others.

Do we really think a bank account is negative dollars?

Like the mother animal some billion years ago finding here young ones gone, missing, is using subtraction. But she is not saying there exists negative young.

So what do we call a missing bank amount? We call it not -$1,112. but rather call it deficit of $1,112.

Now it is easier to write the negative sign "-" than to write deficit, and so we do that convenience ploy. But we should never mistake negative signs as being something "genuine real".

We have let and allowed mathematicians to become philosophers foisting their stupid idealisms upon us and at the threat of failing us, if we dare tell them they are stupid in mathematics.

They were not stupid with A/0 where A is any Real number, positive Real number, and they realized it was undefined. But mathematicians were too stupid to confine negative numbers as also-- undefined.

Now, if you throw out negative numbers. Well then, you have no problems with sqrt-1. Because you never work with negative numbers-- you dispose of them as soon as they arise, just like you dispose of A/0.

So, now, since imaginary numbers can never arise, because you dispose of them. Why in the world have mathematicians spent over 5 centuries worried about a algebra that has solutions? Why were they worried that x^2 = -1 should have a solution? Why not just dispose of all equations like that, as saying, nonsense?

Well, we may say that those 5 centuries were wasted centuries, because mathematicians were too naive to ever look at the big picture-- if division has rooms of "thou shalt not touch" and subtraction is related to division, then subtraction has numbers to ignore as much as we ignore A/0.

The only place in science and wisdom that the negative numbers need be used, is in just a few select spots of science-- physics where you want a negative charge versus a positive charge, other than that, negative numbers are a utter waste of time.

AP

Newsgroups: sci.math
Date: Sun, 18 Jun 2017 22:58:58 -0700 (PDT)

Subject: Re: we ignore A/0, why not ignore all negative numbers Re: may have
found how to get rid of negative numbers
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Mon, 19 Jun 2017 05:58:58 +0000


Re: we ignore A/0, why not ignore all negative numbers Re: may have found how to get rid of negative numbers

Yes now, i believe this is a beautiful solution for negative numbers.
Rule of Negatives: whenever the final answer of a equation is a negative number it is undefined. Only positive number solutions exist.

Tell that to the bank.

Yes, excellent point from a idealist.
Is there negative money? Is there a negative gold coin. Is there a negative paper note to pay for -$1,112.
So what Chris is stumbling over and stumbling upon is his bad case of being brainwashed early in life and now fully accepts the brainwash, and wants to pass that brainwash off on others.
Do we really think a bank account is negative dollars?

Now think for a moment, if all mathematicians for the past 500 years had not all been naive, never looking at the big picture, always looking at the little chickenshat and spending time on shat.

What if there had been just one single mathematician in the past 500 years with his/her eyes on the big picture.

How much different would the Fundamental Theorem of Algebra, have been if we had a big picture guy in math.

Like the mother animal some billion years ago finding here young ones gone, missing, is using subtraction. But she is not saying there exists negative young.
So what do we call a missing bank amount? We call it not -$1,112. but rather call it deficit of $1,112.
Now it is easier to write the negative sign "-" than to write deficit, and so we do that convenience ploy. But we should never mistake negative signs as being something "genuine real".
We have let and allowed mathematicians to become philosophers foisting their stupid idealisms upon us and at the threat of failing us, if we dare tell them they are stupid in mathematics.

So if we had a big picture guy in the past 500 years in Algebra, would have said this-- we cannot use A/0 and call it undefined, that is the internal mechanics of mathematics. And, since division is intricately related to subtraction, means we have wholescale ignoring to do of negative numbers.

That is the Logic behind this. For A/0 is undefined and subtraction is related to division, hence vast amount of negatives are undefined.

And since we cannot be picky choosy on what negatives are undefined, we cannot see a individual negative, means we ignore all negatives. Until, or unless they are a use-- such as physics negative charge, but otherwise-- totally ignore them.

They were not stupid with A/0 where A is any Real number, positive Real number, and they realized it was undefined. But mathematicians were too stupid to confine negative numbers as also-- undefined.
Now, if you throw out negative numbers. Well then, you have no problems with sqrt-1. Because you never work with negative numbers-- you dispose of them as soon as they arise, just like you dispose of A/0.
So, now, since imaginary numbers can never arise, because you dispose of them. Why in the world have mathematicians spent over 5 centuries worried about a algebra that has solutions? Why were they worried that x^2 = -1 should have a solution? Why not just dispose of all equations like that, as saying, nonsense?

So, what would have the history of math been like if no-one bothered with FTA, herds of naive people quibbling over how many solutions for exponent 3?

What would a FTA look like where we obey the rule-- all negatives are undefined and are irrationals and infinites, just occupying Space, but useless to math.

What would a FTA look like under those circumstances?

I have a guess of what a pure true FTA would look like.

Well, we may say that those 5 centuries were wasted centuries, because mathematicians were too naive to ever look at the big picture-- if division has rooms of "thou shalt not touch" and subtraction is related to division, then subtraction has numbers to ignore as much as we ignore A/0.
The only place in science and wisdom that the negative numbers need be used, is in just a few select spots of science-- physics where you want a negative charge versus a positive charge, other than that, negative numbers are a utter waste of time.

I believe the pure and true FTA, where A/0 is undefined and no negative numbers arise, and if they do, they and the entire equation is undefined. So an equation like Y = -x is undefined or x^2 = -1 is undefined. We are never nervous when -5/0 or -1/0 arise for we say, undefined and ignore. But why be crazy when x^2 = -1 arises, and be naive and silly as to think i and -i are solutions.

So, this big picture guy would throw out the equation altogether.

And would ask, of only Positive Valued Equations or Polynomials, what is the pattern of solutions to those?

In Polynomials, only positive valued equations exist, and does that mean for each exponent of a positive valued polynomial have exactly N-1 solutions? Where N is exponent? Or, have just one and only one solution?

So, the real true blue question of Polynomial theory, was, you have a equation with a positive value solution. How many solutions per exponent?

AP

[Archimedes Plutonium]

Alright, I am looking at 4th edition, College Algebra by Stewart, Redlin, Watson, and leafing through pages of polynomials with positive solutions, to try to see if a generalization pattern can be discerned.

For I want a theory of Polynomials where only positive valued solutions can exist and we dismiss all negative crap. Dismiss polynomials that have no positive solution and dismiss all negative valued solutions. The imaginary numbers are dismissed outright.

On page 348

x^3 -3x^2 + x -3

has only one positive valued solution 3

x^3 -2x +4

has no positive valued solution, so we chuck the entire polynomial as invalid

3x^5 +24x^3 + 48x

and has one positive valued solution 0

3x^4 -2x^3 -x^2 -12x -4

Has but one positive valued solution 2

So, the pattern so far is that no matter the size of the exponent, it has but one positive valued solution.

Then, is there a pattern to what equations are tossed out automatically as unable to have a positive solution?

Then, there is the question of what equations that do have a positive value solution, what binds them together as being capable of having a positive valued solution? What is the thread that connects all of the positive valued solution equations?

AP

[Archimedes Plutonium]

Alright, it is easy to spot some patterns already. If the constant term is positive means no positive solution. If the constant is 0 then at least a 0 is solution.

So far, if a positive value solution exists, as far as i can determine it is a one and only one positive value solution. So no matter how large the exponent, only one positive value solution. But that seems too strange and would not bet on it being true. In my distant memory i think i ran into many solutions where both 0 and a different positive value were solutions. So more research.

AP

[Archimedes Plutonium]

Alright, i should think more than look.

Let me build a polynomial with three positive value roots

x (x-1) (x-2) with solutions 0,1,2 and has exponent 3

So there is a chance of getting as robust a FTA as the Old Math.

What is certain and easy to prove is it is impossible to have more solutions than exponent number.

I have the feeling this is going to end up the same as Old Math FTA only without negatives.

AP

[Archimedes Plutonium]

No i was wrong on that evaluation that if the constant is positive it has no solutions as testified by (x-1)(x-2)

So, one would jump to the conclusion that the FTA without negatives has to be far less rich as the FTA with negatives. But it is turning out that positive value only algebra is just as rich.

AP

[Archimedes Plutonium]

Now here i believe some greatness can come from a FTA that deals only with positive number values. An idea that was lost in the fog of Old Math FTA.

So i look at a given polynomial and without doing anything asked whether it has at least one positive number solution. That is the test and major idea-- is there at least one positive valued solution. Well, i lied, for i need to divide.

Before i said if the constant was positive there is no solution but then x^2 -3x +2 instantly is a counterexample. Is that the end of the story on a quick test, a major math theorem? No.

If we look at a arbitrary quadratic, not just the last term, we find our test. But we need to say that all polynomials are just quadratic equations with linear equations.

So if you hand me a x^15 or a x^22 polynomial, or an arbitrary polynomial, i simply start dividing by a x^2 polynomial until nothing remains but a series of x^2 polynomials and perhaps one linear polynomial as a remainder.

This itself is a major theorem that all polynomials are merely a handful of quadratic equations with a linear equation remainder if a remainder is found.

Now, looking at any one of those x^2 polynomials of the arbitrary polynomial and applying the quadratic formula we solve the test.

AP

[Archimedes Plutonium]

Alright, good good good good good. I feel like New Math Algebra beckons, and revolutionizes.

Nothing better in the world, then getting off to a good start, so uplifting.

Our good start is that we allow no negative numbers. The only number we allow that is irrational and infinite is the number 0. For, after all, it is on one side of the equation all be itself in Polynomial theory.

Now, Polynomial theory is only one tiny part of Algebra. Many have the mistaken idea that Algebra is nothing but polynomial theory. Equation theory is larger than polynomial theory, for all polynomials are equations.

Anyway, in Polynomial theory we only allow 0 as a irrational and infinite number. All other numbers are finite rational and positive. Now, do not be mistaken with subtraction and a negative number. So if I had the polynomial x^2 - 3x +2 = 0, do not view that as x^2 + (-3)x +2.

So, our first job in Polynomial theory is see if a polynomial has at LEAST one positive number solution, and we include 0 as positive number solution.

So, we are given a Arbitrary Polynomial, and have to decide in a quick test, if that polynomial has at least one positive number solution. If it does not-- we discard the Polynomial as a fake-polynomial.

Our Polynomial theory is based on only those which have at Least one positive number solution, and, the only solutions are positive numbers. But if a polynomial has no positive number solution, it is not mathematics and we discard the math-nonsense.

A math-nonsense is x^3 -2x +4 = 0

Is that polynomial have at least one positive number solution? The answer is no, it has not one single positive number solution, and we have a quick easy test of any and all polynomials, whether they have at least one positive solution.

TEST:: this test is designed to look at any Arbitrary Polynomial and conclude if at least one positive number solution exists.

What we do, is Group the terms, for we know the sum has to be 0. We Group the positive terms into a first group and then we group the subtraction terms into the second group.


x^3 +4 is first group

-2x is second group

Now we eyeball whether any positive integer can converge or whether they all diverge. We instantly see this polynomial has no positive solution.

Now we look at 3x^4 - 2x^3 - x^2 -12x -4

So, the positive group terms are 3x^4

The subtraction group terms are -2x^3 -x^2 -12x -4

Now we start with the positive integers with 1 then 2 then 3 etc to see if any convergence occurs and we immediately see that at 2 we converge from that of 1 previously, hence, we see this polynomial has at Least one positive solution and we keep it as a true blue Polynomial. It is not a fake polynomial.

So, now, no matter what Arbitrary Polynomial you set before me, the TEST will quickly determine if it is a fake polynomial or true polynomial.

Now, concerning True Polynomials. We have the question of how many solutions a exponent can have and is there a pattern? We know there exists at least One Positive Number valued solution, but is there a general pattern of how many per exponent?

In the polynomial above is a 4th degree polynomial yet it has but one solution. So we know the Old Math FTA rule of exponent number is the number of solutions is not necessarily true in New Math FTA. So, what is the pattern in New Math FTA as per exponent and how many solutions?

We can immediately build a polynomial with exponent 2 that has 2 positive solutions:

(x-1)(x-2)

Or a polynomial of exponent 3 with 3 positive solutions:

(x-1) (x-2) (x-3)

So, what gives? What is New Math's Polynomial theory pattern of positive number value solutions only?

It may well turn out, that the pattern is the same as Old Math's, only with all negative number discarded. And a restriction on the theorem that exponent n has n solutions.

AP

[Archimedes Plutonium]

Alright, this is fun, for instead of culminating to some climax of a Fundamental Theorem of Algebra where we seek at Least One Solution to any polynomial. Here we reversed the situation, in that we start with admitting only polynomials that have at Least one positive valued solution, so there is no need to have a FTA like that of Old Math. But that raises the question of what important theorem exists in this New Math polynomials on par with the FTA of Old Math.

Perhaps, the important theorem in New Math, would concern itself with slopes of polynomials and x and y intercepts. So these two functions Y = 2x +1 and Y = x^3 -2x +4, compared to their polynomials of
2x+1 = 0 and x^3 -2x +4 =0.

So, in polynomial theory, the chasing after solutions, is really what? It is really asking for the x intercept of a function. In this sense, we boil down all of polynomial theory to that of chasing after the x-intercept of a function. And how important could that possibly be? Just a minor detail of a function graph.

So in my two examples, the Y intercept for Y = 2x +1 and Y = x^3 -2x +4 are +1 and +4 respectively. The X-intercept, which would be a solution of the polynomial is when Y= 0. So for 2x+1 the Y intercept is -1/2.

Now, can we pick up the Y intercept for Y = x^3 -2x +4 even though it is not a line function? We know the intercept is -2, but can we get that from the coefficients?

So, what would a FTA of New Math seek, since it already has at Least one positive value solution?

Well, perhaps what it seeks is that every polynomial has one slope Y-intercept.

For example previously given of (x-1)(x-2) = x^2 -3x + 2

This polynomial is not a straightline of Y= mx + b

But we are going to look at it as if it is a straightline and ask for a Y intercept. We know it has solutions of 1 and 2. But can we gather a Y-intercept. Can those coefficients of -3 and 2 give us a Y-intercept?

Can the coefficients of x^3 -2x +4, which are -2 and 4, give us the Y intercept as -2.

So, probably, the FTA theorem in New Math is going to say something like the arbitrary polynomial has at least one Y-intercept of a positive number.

AP

[Archimedes Plutonium]

Y-intercept swallows up polynomial theory Re: What would a Fundamental Theorem of Algebra be like if no negative numbers are allowed

Alright, this is fun, for instead of culminating to some climax of a Fundamental Theorem of Algebra where we seek at Least One Solution to any polynomial. Here we reversed the situation, in that we start with admitting only polynomials that have at Least one positive valued solution, so there is no need to have a FTA like that of Old Math. But that raises the question of what important theorem exists in this New Math polynomials on par with the FTA of Old Math.

Perhaps, the important theorem in New Math, would concern itself with slopes of polynomials and x and y intercepts. So these two functions Y = 2x +1 and Y = x^3 -2x +4, compared to their polynomials of
2x+1 = 0 and x^3 -2x +4 =0.

So, in polynomial theory, the chasing after solutions, is really what? It is really asking for the x intercept of a function. In this sense, we boil down all of polynomial theory to that of chasing after the x-intercept of a function. And how important could that possibly be? Just a minor detail of a function graph.

So in my two examples, the Y intercept for Y = 2x +1 and Y = x^3 -2x +4 are +1 and +4 respectively. The X-intercept, which would be a solution of the polynomial is when Y= 0. So for 2x+1 the X intercept is -1/2.

Now, can we pick up the X intercept for Y = x^3 -2x +4 even though it is not a line function? We know the intercept is -2, but can we get that from the coefficients?

So, what would a FTA of New Math seek, since it already has at Least one positive value solution?

Well, perhaps what it seeks is that every polynomial has one slope X-intercept.

For example previously given of (x-1)(x-2) = x^2 -3x + 2

This polynomial is not a straightline of Y= mx + b

But we are going to look at it as if it is a straightline and ask for a X intercept. We know it has solutions of 1 and 2. But can we gather a X-intercept. Can those coefficients of -3 and 2 give us a X-intercept?

Can the coefficients of x^3 -2x +4, which are -2 and 4, give us the X intercept as -2.

So, probably, the FTA theorem in New Math is going to say something like the arbitrary polynomial has at least one X-intercept of a positive number.

AP

[b***@gmail.com]

I dunno whether Otto Stolz was already careful about negative
numbers, I only checked the following, which has even some
discussion of Euclid in it, and maybe Otto Stolz has
more publications than only this:

Theoretische Arithmetik. Von Otto Stolz und J.A. Gmeiner
by Stolz, Otto, 1842-1905; Gmeiner, Joseph Anton, 1862-
https://archive.org/details/theoretischearit00stoluoft

Also not sure where negative numbers are
burried in Edmund Landaus:

Grundlagen der Analysis
Edmund Landau - 1930

What I didn't find (a PDF link on the web) was "A
translation of Landau's "Grundlagen in AUTOMATH" by
Benthem Jutting, and subsequently not sure whether
something like:

Computer verification of Wiles'
proof of Fermat's Last Theorem
http://www.cs.rug.nl/~wim/fermat/wilesEnglish.html

is already available. Nevertheless it seems that the Dutch
are motivated to do it! So what do we get, who did negative
numbers systematically?

Post by Archimedes Plutonium
Y-intercept swallows up polynomial theory Re: What would a Fundamental Theorem of Algebra be like if no negative numbers are allowed
Alright, this is fun, for instead of culminating to some climax of a Fundamental Theorem of Algebra where we seek at Least One Solution to any polynomial. Here we reversed the situation, in that we start with admitting only polynomials that have at Least one positive valued solution, so there is no need to have a FTA like that of Old Math. But that raises the question of what important theorem exists in this New Math polynomials on par with the FTA of Old Math.
Perhaps, the important theorem in New Math, would concern itself with slopes of polynomials and x and y intercepts. So these two functions Y = 2x +1 and Y = x^3 -2x +4, compared to their polynomials of
2x+1 = 0 and x^3 -2x +4 =0.
So, in polynomial theory, the chasing after solutions, is really what? It is really asking for the x intercept of a function. In this sense, we boil down all of polynomial theory to that of chasing after the x-intercept of a function. And how important could that possibly be? Just a minor detail of a function graph.
So in my two examples, the Y intercept for Y = 2x +1 and Y = x^3 -2x +4 are +1 and +4 respectively. The X-intercept, which would be a solution of the polynomial is when Y= 0. So for 2x+1 the X intercept is -1/2.
Now, can we pick up the X intercept for Y = x^3 -2x +4 even though it is not a line function? We know the intercept is -2, but can we get that from the coefficients?
So, what would a FTA of New Math seek, since it already has at Least one positive value solution?
Well, perhaps what it seeks is that every polynomial has one slope X-intercept.
For example previously given of (x-1)(x-2) = x^2 -3x + 2
This polynomial is not a straightline of Y= mx + b
But we are going to look at it as if it is a straightline and ask for a X intercept. We know it has solutions of 1 and 2. But can we gather a X-intercept. Can those coefficients of -3 and 2 give us a X-intercept?
Can the coefficients of x^3 -2x +4, which are -2 and 4, give us the X intercept as -2.
So, probably, the FTA theorem in New Math is going to say something like the arbitrary polynomial has at least one X-intercept of a positive number.
AP

[b***@gmail.com]

But lets put aside the Dutch, back to the Italians,
this is quite entertaining:

Luca Pacioli: Father of Accounting

Post by b***@gmail.com
I dunno whether Otto Stolz was already careful about negative
numbers, I only checked the following, which has even some
discussion of Euclid in it, and maybe Otto Stolz has
Theoretische Arithmetik. Von Otto Stolz und J.A. Gmeiner
by Stolz, Otto, 1842-1905; Gmeiner, Joseph Anton, 1862-
https://archive.org/details/theoretischearit00stoluoft
Also not sure where negative numbers are
Grundlagen der Analysis
Edmund Landau - 1930
What I didn't find (a PDF link on the web) was "A
translation of Landau's "Grundlagen in AUTOMATH" by
Benthem Jutting, and subsequently not sure whether
Computer verification of Wiles'
proof of Fermat's Last Theorem
http://www.cs.rug.nl/~wim/fermat/wilesEnglish.html
is already available. Nevertheless it seems that the Dutch
are motivated to do it! So what do we get, who did negative
numbers systematically?

Post by Archimedes Plutonium
Y-intercept swallows up polynomial theory Re: What would a Fundamental Theorem of Algebra be like if no negative numbers are allowed
Alright, this is fun, for instead of culminating to some climax of a Fundamental Theorem of Algebra where we seek at Least One Solution to any polynomial. Here we reversed the situation, in that we start with admitting only polynomials that have at Least one positive valued solution, so there is no need to have a FTA like that of Old Math. But that raises the question of what important theorem exists in this New Math polynomials on par with the FTA of Old Math.
Perhaps, the important theorem in New Math, would concern itself with slopes of polynomials and x and y intercepts. So these two functions Y = 2x +1 and Y = x^3 -2x +4, compared to their polynomials of
2x+1 = 0 and x^3 -2x +4 =0.
So, in polynomial theory, the chasing after solutions, is really what? It is really asking for the x intercept of a function. In this sense, we boil down all of polynomial theory to that of chasing after the x-intercept of a function. And how important could that possibly be? Just a minor detail of a function graph.
So in my two examples, the Y intercept for Y = 2x +1 and Y = x^3 -2x +4 are +1 and +4 respectively. The X-intercept, which would be a solution of the polynomial is when Y= 0. So for 2x+1 the X intercept is -1/2.
Now, can we pick up the X intercept for Y = x^3 -2x +4 even though it is not a line function? We know the intercept is -2, but can we get that from the coefficients?
So, what would a FTA of New Math seek, since it already has at Least one positive value solution?
Well, perhaps what it seeks is that every polynomial has one slope X-intercept.
For example previously given of (x-1)(x-2) = x^2 -3x + 2
This polynomial is not a straightline of Y= mx + b
But we are going to look at it as if it is a straightline and ask for a X intercept. We know it has solutions of 1 and 2. But can we gather a X-intercept. Can those coefficients of -3 and 2 give us a X-intercept?
Can the coefficients of x^3 -2x +4, which are -2 and 4, give us the X intercept as -2.
So, probably, the FTA theorem in New Math is going to say something like the arbitrary polynomial has at least one X-intercept of a positive number.
AP

[Archimedes Plutonium]

Post by Archimedes Plutonium
Alright, I am looking at 4th edition, College Algebra by Stewart, Redlin, Watson, and leafing through pages of polynomials with positive solutions, to try to see if a generalization pattern can be discerned.

Alright, what I am looking for is a concept of Polynomial Slope.

Similar to the concept of slope of a line Y = mx + b where the m is the slope

Post by Archimedes Plutonium
For I want a theory of Polynomials where only positive valued solutions can exist and we dismiss all negative crap. Dismiss polynomials that have no positive solution and dismiss all negative valued solutions. The imaginary numbers are dismissed outright.

Why would I want a slope for polynomials?

Because the slope indicates whether a X intercept exists in the 1st Quadrant only, the all positive quadrant.

Post by Archimedes Plutonium
On page 348
x^3 -3x^2 + x -3
has only one positive valued solution 3
x^3 -2x +4
has no positive valued solution, so we chuck the entire polynomial as invalid
3x^5 +24x^3 + 48x
and has one positive valued solution 0
3x^4 -2x^3 -x^2 -12x -4
Has but one positive valued solution 2

Starting page 333

So let me get a few more of these polynomials with solutions from College Algebra

x^3 -x^2 -14x +24 = 0

has positive valued solutions 2, 3. Note that 24 is 2*3*4 for -4 is a solution


x^3 -3x +2 = 0

solutions are 1, -2


2x^3 + x^2 -13x +6 = 0

factor of constant term/factor of leading coefficient is according to Rational Zeros Theorem, possible rational zero

+- of 1, 2, 3, 6, then +- 1,2

So, +- 1,2,3,6,1/2, 3/2

We find 2 is a solution

Post by Archimedes Plutonium
So, the pattern so far is that no matter the size of the exponent, it has but one positive valued solution.
Then, is there a pattern to what equations are tossed out automatically as unable to have a positive solution?
Then, there is the question of what equations that do have a positive value solution, what binds them together as being capable of having a positive valued solution? What is the thread that connects all of the positive valued solution equations?

What I am doing here is trying to find the easiest way of spotting if a polynomial has a positive value solution, via a slope for the X-intercept

I need to define a Slope of Polynomial, and there is this theorem of leading coefficient with ending constant. So if the leading number and ending number play a role in what solutions exist, then it is highly likely a concept of Polynomial Slope exists.

x^4 -5x^3 -5x^2 + 23x + 10

+- 1,2,5,10

Solution is 5

Old Math solutions in full were 5, -2, 2.4, and -.4


More to use to test

2x^5 + 5x^4 - 8x^3 -14x^2 + 6x + 9

has solutions of 1 and 3/2

So, if I define the General Polynomial Slope as this for the above case example

factors 9/factors 2 *(x) = Slope of polynomial

AP

[Archimedes Plutonium]

Alright this is working out nicely, really nice, in that what the FTA of Old Math was worried about is that at least one solution to every polynomial exists. In New Math, we see that as crazy because in New Math, in order to qualify as being a true blue polynomial, you have to have a Positive Valued solution in the first place, otherwise you are thrown in the trash can as a "fakery polynomial". A polynomial like x^2 +1 is a fake polynomial.

So, then, in New Math, we thus have a problem of what can a FTA be about? It cannot be about having at least one positive valued solution for that is the requirement of being a valid polynomial in the first place. So what should a FTA in New Math concern itself about?

Some possibilities is that the FTA concerns::

i) how many solutions of positive valued Rational numbers exist per exponent?

That is a concern, because in Old Math, they had a tidy result that the exponent degree meant exactly that number of solutions. So if the exponent is 5, there are 5 zero solutions to the polynomial.

In New Math, the number of exponents may vary and not dependent on exponent size.

So what is another possible FTA in New Math?

The one I favor is this one, for the time being anyway.

ii) The FTA in New Math says the Polynomial Slope is a line equation Y = mx+b, using the leading and ending coefficients, such forming the X-intercept of the first positive value solution.

For example, the polynomial (x-2) (x-3) (x-4) is a 3rd degree polynomial exponent 3 and has solutions 2, 3, 4. And as such, a Slope of a line equation involving leading coefficient which is 1 and involving 2 of that polynomial should look like this x -2 of a Y = mx+ b, in addition to more slopes of that same polynomial.

AP

[Archimedes Plutonium]

On Tuesday, June 20, 2017 at 1:23:06 AM UTC-5, Archimedes Plutonium wrote:
(snipped)

Post by Archimedes Plutonium
ii) The FTA in New Math says the Polynomial Slope is a line equation Y = mx+b, using the leading and ending coefficients, such forming the X-intercept of the first positive value solution.

yes, I think this is what the FTA of New Math wanted, something unique-- a unique first slope with X-intercept

Post by Archimedes Plutonium
For example, the polynomial (x-2) (x-3) (x-4) is a 3rd degree polynomial exponent 3 and has solutions 2, 3, 4. And as such, a Slope of a line equation involving leading coefficient which is 1 and involving 2 of that polynomial should look like this x -2 of a Y = mx+ b, in addition to more slopes of that same polynomial.

Alright, that polynomial is x^3 -9x^2 + 26x -24

Now, by sheer inspection, can I perceive that it contains a Y = mx+b as that of x-2?

Of course, and I can perceive x-1, and x-3, and x-4, and x-6, and x-8 and x-12 because leading and ending coefficients were 1 and 24.

So, from sheer inspection I can ask, well, what is the first solution that is positive? Trying x-1, I see it does not work, thence trying x-2 I find it works.

So, now, take the ARBITRARY Polynomial, having gone through the test of whether it is a fake or true polynomial and found to be True Polynomial. Now, we apply a FTA upon this polynomial.

We take the leading and ending coefficient and list the total possible factors, x-1 will always be on the list (now x=0 is obvious, so we ignore that case) and we see if x=1 is a solution and end of work. If not a solution we look at the next larger factor of coefficient and try that one out, until we have a Linear equation Y = mx +b where the -b is the positive valued solution, the X-intercept to the Polynomial.

So here the concern is more of the X-intercept than it is any concern of the Slope, so I overemphasized the slope.

AP

[Archimedes Plutonium]

Post by Archimedes Plutonium
Alright, that polynomial is x^3 -9x^2 + 26x -24

Alright, this was nice fine and dandy, you would agree, for not much pain was involved. And, where Galois and Gauss spent a lifetime in solving Algebra polynomials, we spend a weekend. We have much more tougher work ahead, then to spend a lifetime on a corner of Algebra.

But in solving something, inevitably leads to newer problems.

The problem now is whether we can Generalize the Arbitrary Polynomial into its most basic components of Linear line segments Y = mx + b.

In that polynomial above x^3 -9x^2 + 26x -24 is factorable into the nice well behaved Line Segments of (x-2)(x-3)(x-4).

Now if you guess that most polynomials are not well behaved, you are correct. Few polynomials dissolve into pure straightline segments, their atoms of the polynomial in question. We want to atomize the Arbitrary Polynomial.

So, now what if I did not know the factors of x^3 -9x^2 + 26x -24, can I atomize that polynomial without knowing its factors.

So, what if I did this:

x(x^2 - 9x) + 26x -24

then this

(x)(x)(x-9) + 26x -24

next I do this

(x)(x)(x-9) + 2(13x -12)

And that is about all I can do. And this sort of thing is very easy to do on all and any Arbitrary Polynomial, especially those with a huge exponent involved, where we atomize the polynomial. For most polynomials do not have nice clear cut factors. So I atomize rather than factorize. Atomize takes a fraction of a minute whereas factoring could take a half hour.

Now we know the factors of the above as (x-2)(x-3)(x-4)

in stark contrast to (x)(x)(x-9) + 2(13x -12) for which we focus on the two line segments Y= mx+b of that of (x-9) and (13x-12)

We ask, can we arrive at our FTA solution of X-intercept at +2 from that of (13x-12)

I think we can, in that the factors of 12 are 1,2,3,4, and one by one we eliminate the 1 as a solution and find that 2 is the first solution and then 3 and 4 are also solutions.

Now, let me check on some given by Stewart,Redlin, Watson

x^4 -5x^3 -5x^2 + 23x + 10

+- 1,2,5,10

Solution is 5

Old Math solutions in full were 5, -2, 2.4, and -.4

Here we have (x)(x)(x)(x-5) - (5)(x)(x+23) no, this does not work, I need always have the last two terms form a Line Segment

(x)(x)(x)(x-5) - (5)(x)(x) + (23x +10)

And here my possible X-intercepts are

5 and 2 and 5 again. The 2 does not work so 5 works and thus, is the first line segment that forms a X-intercept


More to use to test

2x^5 + 5x^4 - 8x^3 -14x^2 + 6x + 9

has solutions of 1 and 3/2

Here I have (x)(x)(x)(x) (2x+5) - 8x^3 - 14x^2 + (6x+9)

Here i never even bothered with middle terms for they are mostly out of the picture. Apparently, solutions involve the two endpoints the leading coefficient and the ending and the middle terms are just plain adjustments, irrelevant.

Now, possible solutions in order of size are 1, 3/2, 5/2, 3, 5

And we find that 1 and 3/2 are true solutions.

Now, let me see if this method can prove if a Fake Polynomial happens to sneek through and is now looking for its First X-intercept.

The polynomial x^3 - 2x +4

Suppose that polynomial got past all security check points and not thrown out as a Fake Polynomial. And suppose it is now being tested for its First X-intercept

So we have (x)(x)(x) - (2x + 4)

So, its factors would be for a possible solution are 1, 2, 4. The 1 does not work, neither does 2 or 4.

Hence, we found this polynomial a fake polynomial and throw it in the trash.

AP

[Archimedes Plutonium]

Yes, I am almost done here. The Aesop fable for this lesson, is that when you do fake science, it consumes a lifetime-- Gauss, Galois (although Galois had a interrupted lifetime). But when dabbling in fakery in science, is like a liaring, the liaring has to continue and continue, it can not stop, because the truth of the matter is constantly knocking on the front door.

When you propose negative numbers into math, you are liaring about reality, and when you propose sqrt-1 into math you are liaring about reality.

When you discard the negative numbers you get a whole new and different Fundamental Theorem of Algebra. You get a clean, nice neat and fancy Polynomial theory, easy to learn in a weekend.

And when you discard negative numbers, well, of course you never need the horrible liaring of a imaginary number sqrt-1.

True Blue Math is easy, simple straightforward. Liaring fakery math is a constant patching up of crap and garbage. And a total waste of time and energy. How much time in graduate school are students subjected to the nightmarish liarings of sqrt-1 and negative numbers.

I was reading a article recently in NEW SCIENTIST, 10June2017, page 42 Poisoner-in-chief "Meet the one-man environmental disaster" the story of Thomas Midgley. The chemist that pushed the use of tetraethyllead additive in gasoline, poisoning the environment with lead, and the pusher of CFC as a refrigerant. CFC caused ozone depletion.

Midgley was a one man wrecking ball of the Earth's environment.

Not that his inventions were fakery, but, like math, a lot of clean-up of pollution has to take place to get things back "to right and order".

AP

[b***@gmail.com]

By "The Aesop fable for this lesson, is that when you do
fake science, it consumes a lifetime" you are talking about
your own brain farts? No math for 30 years?

Post by Archimedes Plutonium
Yes, I am almost done here. The Aesop fable for this lesson, is that when you do fake science, it consumes a lifetime-- Gauss, Galois (although Galois had a interrupted lifetime). But when dabbling in fakery in science, is like a liaring, the liaring has to continue and continue, it can not stop, because the truth of the matter is constantly knocking on the front door.
When you propose negative numbers into math, you are liaring about reality, and when you propose sqrt-1 into math you are liaring about reality.
When you discard the negative numbers you get a whole new and different Fundamental Theorem of Algebra. You get a clean, nice neat and fancy Polynomial theory, easy to learn in a weekend.
And when you discard negative numbers, well, of course you never need the horrible liaring of a imaginary number sqrt-1.
True Blue Math is easy, simple straightforward. Liaring fakery math is a constant patching up of crap and garbage. And a total waste of time and energy. How much time in graduate school are students subjected to the nightmarish liarings of sqrt-1 and negative numbers.
I was reading a article recently in NEW SCIENTIST, 10June2017, page 42 Poisoner-in-chief "Meet the one-man environmental disaster" the story of Thomas Midgley. The chemist that pushed the use of tetraethyllead additive in gasoline, poisoning the environment with lead, and the pusher of CFC as a refrigerant. CFC caused ozone depletion.
Midgley was a one man wrecking ball of the Earth's environment.
Not that his inventions were fakery, but, like math, a lot of clean-up of pollution has to take place to get things back "to right and order".
AP

[Archimedes Plutonium]

So, is there any indication, any sign that you have a fakery of imaginary numbers and of Fundamental Theorem of Algebra of Old Math?

Yes, there are two obvious signs of fakery::

A) you cannot graph imaginaries with Reals for where in the heck do you locate something like i+1 or even i?

B) When you have as many solutions as the degree of exponent, tells you, that something plastic is going on, not something genuine. Why should a exponent have any relationship with the number of solutions. It should not.

AP

[b***@gmail.com]

Wolfram alpha uses two colors:
https://www.wolframalpha.com/input/?i=x^%281%2F2%29

But this is way to high above your head, since
you are a complete imbecil and a spammer a**hole.

Post by Archimedes Plutonium
A) you cannot graph imaginaries with Reals for where in the heck do you locate something like i+1 or even i?

[b***@gmail.com]

As long as these two mappings related to multiplication are
injective, there are not many chances that this relationship
with the degree (=max exponent of polynomial) changes:

left_x : C -> C, x <> 0
left_x(y) = x*y

right_y : C -> C, y <> 0
right_y(x) = x*y

They are injective, arent they? There are a few more reasons
I guess, relating to the number of solutions...

Post by Archimedes Plutonium
B) When you have as many solutions as the degree of exponent, tells you, that something plastic is going on, not something genuine. Why should a exponent have any relationship with the number of solutions. It should not.

[b***@gmail.com]

Only fields have this injectivity, but rings do not necessarily
have it, as a result a polynomial in a ring can have more solutions
than the degree says:

"The usual factorization tricks always work, if p is a prime. However, note that some rings have zero divisors. For example 2⋅4≡0(mod8), so the polynomial x2−1=(x−1)(x+1) has 3 as a root in the ring Z8, even though (3−1)=2 and (3+1)=4 are both non-zero. In fact, it is not hard to see that this polynomial has exactly 4 zeros in the ring Z8."

https://math.stackexchange.com/a/44783/4414

Post by b***@gmail.com
As long as these two mappings related to multiplication are
injective, there are not many chances that this relationship
left_x : C -> C, x <> 0
left_x(y) = x*y
right_y : C -> C, y <> 0
right_y(x) = x*y
They are injective, arent they? There are a few more reasons
I guess, relating to the number of solutions...

Post by Archimedes Plutonium
B) When you have as many solutions as the degree of exponent, tells you, that something plastic is going on, not something genuine. Why should a exponent have any relationship with the number of solutions. It should not.

[b***@gmail.com]

Interestingly there are the waters of
Kaplansky's conjecture (on group rings):
https://en.wikipedia.org/wiki/Kaplansky's_conjecture

From 1968? Still unsolved, as of now 2017?

Post by b***@gmail.com
Only fields have this injectivity, but rings do not necessarily
have it, as a result a polynomial in a ring can have more solutions
"The usual factorization tricks always work, if p is a prime. However, note that some rings have zero divisors. For example 2⋅4≡0(mod8), so the polynomial x2−1=(x−1)(x+1) has 3 as a root in the ring Z8, even though (3−1)=2 and (3+1)=4 are both non-zero. In fact, it is not hard to see that this polynomial has exactly 4 zeros in the ring Z8."
https://math.stackexchange.com/a/44783/4414

Post by b***@gmail.com
As long as these two mappings related to multiplication are
injective, there are not many chances that this relationship
left_x : C -> C, x <> 0
left_x(y) = x*y
right_y : C -> C, y <> 0
right_y(x) = x*y
They are injective, arent they? There are a few more reasons
I guess, relating to the number of solutions...

Post by Archimedes Plutonium
B) When you have as many solutions as the degree of exponent, tells you, that something plastic is going on, not something genuine. Why should a exponent have any relationship with the number of solutions. It should not.

[Archimedes Plutonium]

Post by b***@gmail.com
Only fields have this injectivity, but rings do not necessarily

Math failure, Burse, asks for more details

Newsgroups: sci.math
Date: Tue, 20 Jun 2017 00:25:04 -0700 (PDT)

Subject: FTA of New Math shaping up to be the First positive solution as a
linear segment Re: What would a Fundamental Theorem of Algebra be like if no
negative numbers are allowed
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Tue, 20 Jun 2017 07:25:04 +0000


FTA of New Math shaping up to be the First positive solution as a linear segment Re: What would a Fundamental Theorem of Algebra be like if no negative numbers are allowed

Post by b***@gmail.com
Alright, that polynomial is x^3 -9x^2 + 26x -24

Alright, this was nice fine and dandy, you would agree, for not much pain was involved. And, where Galois and Gauss spent a lifetime in solving Algebra polynomials, we spend a weekend. We have much more tougher work ahead, then to spend a lifetime on a corner of Algebra.

But in solving something, inevitably leads to newer problems.

The problem now is whether we can Generalize the Arbitrary Polynomial into its most basic components of Linear line segments Y = mx + b.

In that polynomial above x^3 -9x^2 + 26x -24 is factorable into the nice well behaved Line Segments of (x-2)(x-3)(x-4).

Now if you guess that most polynomials are not well behaved, you are correct. Few polynomials dissolve into pure straightline segments, their atoms of the polynomial in question. We want to atomize the Arbitrary Polynomial.

So, now what if I did not know the factors of x^3 -9x^2 + 26x -24, can I atomize that polynomial without knowing its factors.

So, what if I did this:

x(x^2 - 9x) + 26x -24

then this

(x)(x)(x-9) + 26x -24

next I do this

(x)(x)(x-9) + 2(13x -12)

And that is about all I can do. And this sort of thing is very easy to do on all and any Arbitrary Polynomial, especially those with a huge exponent involved, where we atomize the polynomial. For most polynomials do not have nice clear cut factors. So I atomize rather than factorize. Atomize takes a fraction of a minute whereas factoring could take a half hour.

Now we know the factors of the above as (x-2)(x-3)(x-4)

in stark contrast to (x)(x)(x-9) + 2(13x -12) for which we focus on the two line segments Y= mx+b of that of (x-9) and (13x-12)

We ask, can we arrive at our FTA solution of X-intercept at +2 from that of (13x-12)

I think we can, in that the factors of 12 are 1,2,3,4, and one by one we eliminate the 1 as a solution and find that 2 is the first solution and then 3 and 4 are also solutions.

Now, let me check on some given by Stewart,Redlin, Watson

x^4 -5x^3 -5x^2 + 23x + 10

+- 1,2,5,10

Solution is 5

Old Math solutions in full were 5, -2, 2.4, and -.4

Here we have (x)(x)(x)(x-5) - (5)(x)(x+23) no, this does not work, I need always have the last two terms form a Line Segment

(x)(x)(x)(x-5) - (5)(x)(x) + (23x +10)

And here my possible X-intercepts are

5 and 2 and 5 again. The 2 does not work so 5 works and thus, is the first line segment that forms a X-intercept


More to use to test

2x^5 + 5x^4 - 8x^3 -14x^2 + 6x + 9

has solutions of 1 and 3/2

Here I have (x)(x)(x)(x) (2x+5) - 8x^3 - 14x^2 + (6x+9)

Here i never even bothered with middle terms for they are mostly out of the picture. Apparently, solutions involve the two endpoints the leading coefficient and the ending and the middle terms are just plain adjustments, irrelevant.

Now, possible solutions in order of size are 1, 3/2, 5/2, 3, 5

And we find that 1 and 3/2 are true solutions.

Now, let me see if this method can prove if a Fake Polynomial happens to sneek through and is now looking for its First X-intercept.

The polynomial x^3 - 2x +4

Suppose that polynomial got past all security check points and not thrown out as a Fake Polynomial. And suppose it is now being tested for its First X-intercept

So we have (x)(x)(x) - (2x + 4)

So, its factors would be for a possible solution are 1, 2, 4. The 1 does not work, neither does 2 or 4.

Hence, we found this polynomial a fake polynomial and throw it in the trash.

AP

Newsgroups: sci.math
Date: Tue, 20 Jun 2017 00:45:55 -0700 (PDT)

Subject: The True Blue Algebra, not the fake algebra with its negative numbers
and its imaginary numbers
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Tue, 20 Jun 2017 07:45:55 +0000



The True Blue Algebra, not the fake algebra with its negative numbers and its imaginary numbers

Yes, I am almost done here. The Aesop fable for this lesson, is that when you do fake science, it consumes a lifetime-- Gauss, Galois (although Galois had a interrupted lifetime). But when dabbling in fakery in science, is like a liaring, the liaring has to continue and continue, it can not stop, because the truth of the matter is constantly knocking on the front door.

When you propose negative numbers into math, you are liaring about reality, and when you propose sqrt-1 into math you are liaring about reality.

When you discard the negative numbers you get a whole new and different Fundamental Theorem of Algebra. You get a clean, nice neat and fancy Polynomial theory, easy to learn in a weekend.

And when you discard negative numbers, well, of course you never need the horrible liaring of a imaginary number sqrt-1.

True Blue Math is easy, simple straightforward. Liaring fakery math is a constant patching up of crap and garbage. And a total waste of time and energy. How much time in graduate school are students subjected to the nightmarish liarings of sqrt-1 and negative numbers.

I was reading a article recently in NEW SCIENTIST, 10June2017, page 42 Poisoner-in-chief "Meet the one-man environmental disaster" the story of Thomas Midgley. The chemist that pushed the use of tetraethyllead additive in gasoline, poisoning the environment with lead, and the pusher of CFC as a refrigerant. CFC caused ozone depletion.

Midgley was a one man wrecking ball of the Earth's environment.

Not that his inventions were fakery, but, like math, a lot of clean-up of pollution has to take place to get things back "to right and order".

AP

Newsgroups: sci.math
Date: Tue, 20 Jun 2017 02:15:46 -0700 (PDT)

Subject: two obvious signs of fakery Re: The True Blue Algebra, not the fake
algebra with its negative numbers and its imaginary numbers
From: Archimedes Plutonium <***@gmail.com>
Injection-Date: Tue, 20 Jun 2017 09:15:46 +0000


two obvious signs of fakery Re: The True Blue Algebra, not the fake algebra with its negative numbers and its imaginary numbers

So, is there any indication, any sign that you have a fakery of imaginary numbers and of Fundamental Theorem of Algebra of Old Math?

Yes, there are two obvious signs of fakery::

A) you cannot graph imaginaries with Reals for where in the heck do you locate something like i+1 or even i?

B) When you have as many solutions as the degree of exponent, tells you, that something plastic is going on, not something genuine. Why should a exponent have any relationship with the number of solutions. It should not.

AP

[bassam king karzeddin]

Post by Archimedes Plutonium
Newsgroups: sci.math
Date: Sun, 18 Jun 2017 22:23:11 -0700 (PDT)
Subject: we ignore A/0, why not ignore all negative numbers Re: may have found
how to get rid of negative numbers
Injection-Date: Mon, 19 Jun 2017 05:23:11 +0000
we ignore A/0, why not ignore all negative numbers Re: may have found how to get rid of negative numbers
- show quoted text -
Yes, excellent point from a idealist.
Is there negative money? Is there a negative gold coin. Is there a negative paper note to pay for -$1,112.
So what Chris is stumbling over and stumbling upon is his bad case of being brainwashed early in life and now fully accepts the brainwash, and wants to pass that brainwash off on others.
Do we really think a bank account is negative dollars?
Like the mother animal some billion years ago finding here young ones gone, missing, is using subtraction. But she is not saying there exists negative young.
So what do we call a missing bank amount? We call it not -$1,112. but rather call it deficit of $1,112.
Now it is easier to write the negative sign "-" than to write deficit, and so we do that convenience ploy. But we should never mistake negative signs as being something "genuine real".
We have let and allowed mathematicians to become philosophers foisting their stupid idealisms upon us and at the threat of failing us, if we dare tell them they are stupid in mathematics.
They were not stupid with A/0 where A is any Real number, positive Real number, and they realized it was undefined. But mathematicians were too stupid to confine negative numbers as also-- undefined.
Now, if you throw out negative numbers. Well then, you have no problems with sqrt-1. Because you never work with negative numbers-- you dispose of them as soon as they arise, just like you dispose of A/0.
So, now, since imaginary numbers can never arise, because you dispose of them. Why in the world have mathematicians spent over 5 centuries worried about a algebra that has solutions? Why were they worried that x^2 = -1 should have a solution? Why not just dispose of all equations like that, as saying, nonsense?
Well, we may say that those 5 centuries were wasted centuries, because mathematicians were too naive to ever look at the big picture-- if division has rooms of "thou shalt not touch" and subtraction is related to division, then subtraction has numbers to ignore as much as we ignore A/0.
The only place in science and wisdom that the negative numbers need be used, is in just a few select spots of science-- physics where you want a negative charge versus a positive charge, other than that, negative numbers are a utter waste of time.
AP
Newsgroups: sci.math
Date: Sun, 18 Jun 2017 22:58:58 -0700 (PDT)
Subject: Re: we ignore A/0, why not ignore all negative numbers Re: may have
found how to get rid of negative numbers
Injection-Date: Mon, 19 Jun 2017 05:58:58 +0000
Re: we ignore A/0, why not ignore all negative numbers Re: may have found how to get rid of negative numbers

Post by Archimedes Plutonium

Yes now, i believe this is a beautiful solution for negative numbers.
Rule of Negatives: whenever the final answer of a equation is a negative number it is undefined. Only positive number solutions exist.

Tell that to the bank.

Yes, excellent point from a idealist.
Is there negative money? Is there a negative gold coin. Is there a negative paper note to pay for -$1,112.
So what Chris is stumbling over and stumbling upon is his bad case of being brainwashed early in life and now fully accepts the brainwash, and wants to pass that brainwash off on others.
Do we really think a bank account is negative dollars?

Now think for a moment, if all mathematicians for the past 500 years had not all been naive, never looking at the big picture, always looking at the little chickenshat and spending time on shat.
What if there had been just one single mathematician in the past 500 years with his/her eyes on the big picture.
How much different would the Fundamental Theorem of Algebra, have been if we had a big picture guy in math.

Post by Archimedes Plutonium
Like the mother animal some billion years ago finding here young ones gone, missing, is using subtraction. But she is not saying there exists negative young.
So what do we call a missing bank amount? We call it not -$1,112. but rather call it deficit of $1,112.
Now it is easier to write the negative sign "-" than to write deficit, and so we do that convenience ploy. But we should never mistake negative signs as being something "genuine real".
We have let and allowed mathematicians to become philosophers foisting their stupid idealisms upon us and at the threat of failing us, if we dare tell them they are stupid in mathematics.

So if we had a big picture guy in the past 500 years in Algebra, would have said this-- we cannot use A/0 and call it undefined, that is the internal mechanics of mathematics. And, since division is intricately related to subtraction, means we have wholescale ignoring to do of negative numbers.
That is the Logic behind this. For A/0 is undefined and subtraction is related to division, hence vast amount of negatives are undefined.
And since we cannot be picky choosy on what negatives are undefined, we cannot see a individual negative, means we ignore all negatives. Until, or unless they are a use-- such as physics negative charge, but otherwise-- totally ignore them.

Post by Archimedes Plutonium
They were not stupid with A/0 where A is any Real number, positive Real number, and they realized it was undefined. But mathematicians were too stupid to confine negative numbers as also-- undefined.
Now, if you throw out negative numbers. Well then, you have no problems with sqrt-1. Because you never work with negative numbers-- you dispose of them as soon as they arise, just like you dispose of A/0.
So, now, since imaginary numbers can never arise, because you dispose of them. Why in the world have mathematicians spent over 5 centuries worried about a algebra that has solutions? Why were they worried that x^2 = -1 should have a solution? Why not just dispose of all equations like that, as saying, nonsense?

So, what would have the history of math been like if no-one bothered with FTA, herds of naive people quibbling over how many solutions for exponent 3?
What would a FTA look like where we obey the rule-- all negatives are undefined and are irrationals and infinites, just occupying Space, but useless to math.
What would a FTA look like under those circumstances?
I have a guess of what a pure true FTA would look like.

Post by Archimedes Plutonium
Well, we may say that those 5 centuries were wasted centuries, because mathematicians were too naive to ever look at the big picture-- if division has rooms of "thou shalt not touch" and subtraction is related to division, then subtraction has numbers to ignore as much as we ignore A/0.
The only place in science and wisdom that the negative numbers need be used, is in just a few select spots of science-- physics where you want a negative charge versus a positive charge, other than that, negative numbers are a utter waste of time.

I believe the pure and true FTA, where A/0 is undefined and no negative numbers arise, and if they do, they and the entire equation is undefined. So an equation like Y = -x is undefined or x^2 = -1 is undefined. We are never nervous when -5/0 or -1/0 arise for we say, undefined and ignore. But why be crazy when x^2 = -1 arises, and be naive and silly as to think i and -i are solutions.
So, this big picture guy would throw out the equation altogether.
And would ask, of only Positive Valued Equations or Polynomials, what is the pattern of solutions to those?
In Polynomials, only positive valued equations exist, and does that mean for each exponent of a positive valued polynomial have exactly N-1 solutions? Where N is exponent? Or, have just one and only one solution?
So, the real true blue question of Polynomial theory, was, you have a equation with a positive value solution. How many solutions per exponent?
AP

We know that most of the well-established mathematics actually not any real science but for fun and entertainments of few peculiar and abnormal people who generally produce SH*T

And those Sh*ty objects are occupying most of the volumes of maths today, ranging from negative concept to imaginary concept, to infinite concept, then creating so many fictions as transcendental numbers to algebraic numbers to fiction angles, to space and multi-dimensional universe, to more fictions extended from maths to physics such as negative mass, negative speed, imaginary mass or acceleration, to time travel to so many obvious unbelievable fiction stories

And we know that the real maths is actually a real science that requires
very rare talent that truly may not be available at all

So, naturally, such many legend stories must then arise particularly from those people whom they considered as managers or moderators of mathematics for sure

The best joke of all is that negative (XYZ) space Coordinations around your heads, wonder!

And I keep asking myself with so much amusement

Are the Top Professional Mathematicians are indeed participating proudly for so many centuries and so shamelessly in the biggest race of "Who is the most foolish", Wonder!

However, I had explained enough and quite many times this unlimited level of mathematicians stupidity in my posts for sure

BKK

[Archimedes Plutonium]

Yes BKK keep up the good work.

Math is polluted and needs very much a shower and bath.

Read the other day of a chemist who invented two of the worlds most polluting chemicals -- lead for gasoline to stop the banging and then CFC that almost destroyed the ozone.

Much of Old Time math is sheer pollution told by imbeciles seeking fame -- not Truth.

Keep up the good work.

Sadly, the world seems never able to reward those that clean up the place-- only those who pollute more.

[Simon Roberts]

Post by Archimedes Plutonium
Newsgroups: sci.math
Date: Sun, 18 Jun 2017 22:23:11 -0700 (PDT)
Subject: we ignore A/0, why not ignore all negative numbers Re: may have found
how to get rid of negative numbers
Injection-Date: Mon, 19 Jun 2017 05:23:11 +0000
we ignore A/0, why not ignore all negative numbers Re: may have found how to get rid of negative numbers
- show quoted text -
Yes, excellent point from a idealist.
Is there negative money? Is there a negative gold coin. Is there a negative paper note to pay for -$1,112.
So what Chris is stumbling over and stumbling upon is his bad case of being brainwashed early in life and now fully accepts the brainwash, and wants to pass that brainwash off on others.
Do we really think a bank account is negative dollars?
Like the mother animal some billion years ago finding here young ones gone, missing, is using subtraction. But she is not saying there exists negative young.
So what do we call a missing bank amount? We call it not -$1,112. but rather call it deficit of $1,112.
Now it is easier to write the negative sign "-" than to write deficit, and so we do that convenience ploy. But we should never mistake negative signs as being something "genuine real".
We have let and allowed mathematicians to become philosophers foisting their stupid idealisms upon us and at the threat of failing us, if we dare tell them they are stupid in mathematics.
They were not stupid with A/0 where A is any Real number, positive Real number, and they realized it was undefined. But mathematicians were too stupid to confine negative numbers as also-- undefined.
Now, if you throw out negative numbers. Well then, you have no problems with sqrt-1. Because you never work with negative numbers-- you dispose of them as soon as they arise, just like you dispose of A/0.
So, now, since imaginary numbers can never arise, because you dispose of them. Why in the world have mathematicians spent over 5 centuries worried about a algebra that has solutions? Why were they worried that x^2 = -1 should have a solution? Why not just dispose of all equations like that, as saying, nonsense?
Well, we may say that those 5 centuries were wasted centuries, because mathematicians were too naive to ever look at the big picture-- if division has rooms of "thou shalt not touch" and subtraction is related to division, then subtraction has numbers to ignore as much as we ignore A/0.
The only place in science and wisdom that the negative numbers need be used, is in just a few select spots of science-- physics where you want a negative charge versus a positive charge, other than that, negative numbers are a utter waste of time.
AP
Newsgroups: sci.math
Date: Sun, 18 Jun 2017 22:58:58 -0700 (PDT)
Subject: Re: we ignore A/0, why not ignore all negative numbers Re: may have
found how to get rid of negative numbers
Injection-Date: Mon, 19 Jun 2017 05:58:58 +0000
Re: we ignore A/0, why not ignore all negative numbers Re: may have found how to get rid of negative numbers

Post by Archimedes Plutonium

Yes now, i believe this is a beautiful solution for negative numbers.
Rule of Negatives: whenever the final answer of a equation is a negative number it is undefined. Only positive number solutions exist.

Tell that to the bank.

Yes, excellent point from a idealist.
Is there negative money? Is there a negative gold coin. Is there a negative paper note to pay for -$1,112.
So what Chris is stumbling over and stumbling upon is his bad case of being brainwashed early in life and now fully accepts the brainwash, and wants to pass that brainwash off on others.
Do we really think a bank account is negative dollars?

Now think for a moment, if all mathematicians for the past 500 years had not all been naive, never looking at the big picture, always looking at the little chickenshat and spending time on shat.
What if there had been just one single mathematician in the past 500 years with his/her eyes on the big picture.
How much different would the Fundamental Theorem of Algebra, have been if we had a big picture guy in math.

Post by Archimedes Plutonium
Like the mother animal some billion years ago finding here young ones gone, missing, is using subtraction. But she is not saying there exists negative young.
So what do we call a missing bank amount? We call it not -$1,112. but rather call it deficit of $1,112.
Now it is easier to write the negative sign "-" than to write deficit, and so we do that convenience ploy. But we should never mistake negative signs as being something "genuine real".
We have let and allowed mathematicians to become philosophers foisting their stupid idealisms upon us and at the threat of failing us, if we dare tell them they are stupid in mathematics.

So if we had a big picture guy in the past 500 years in Algebra, would have said this-- we cannot use A/0 and call it undefined, that is the internal mechanics of mathematics. And, since division is intricately related to subtraction, means we have wholescale ignoring to do of negative numbers.
That is the Logic behind this. For A/0 is undefined and subtraction is related to division, hence vast amount of negatives are undefined.
And since we cannot be picky choosy on what negatives are undefined, we cannot see a individual negative, means we ignore all negatives. Until, or unless they are a use-- such as physics negative charge, but otherwise-- totally ignore them.

Post by Archimedes Plutonium
They were not stupid with A/0 where A is any Real number, positive Real number, and they realized it was undefined. But mathematicians were too stupid to confine negative numbers as also-- undefined.
Now, if you throw out negative numbers. Well then, you have no problems with sqrt-1. Because you never work with negative numbers-- you dispose of them as soon as they arise, just like you dispose of A/0.
So, now, since imaginary numbers can never arise, because you dispose of them. Why in the world have mathematicians spent over 5 centuries worried about a algebra that has solutions? Why were they worried that x^2 = -1 should have a solution? Why not just dispose of all equations like that, as saying, nonsense?

So, what would have the history of math been like if no-one bothered with FTA, herds of naive people quibbling over how many solutions for exponent 3?
What would a FTA look like where we obey the rule-- all negatives are undefined and are irrationals and infinites, just occupying Space, but useless to math.
What would a FTA look like under those circumstances?
I have a guess of what a pure true FTA would look like.

Post by Archimedes Plutonium
Well, we may say that those 5 centuries were wasted centuries, because mathematicians were too naive to ever look at the big picture-- if division has rooms of "thou shalt not touch" and subtraction is related to division, then subtraction has numbers to ignore as much as we ignore A/0.
The only place in science and wisdom that the negative numbers need be used, is in just a few select spots of science-- physics where you want a negative charge versus a positive charge, other than that, negative numbers are a utter waste of time.

I believe the pure and true FTA, where A/0 is undefined and no negative numbers arise, and if they do, they and the entire equation is undefined. So an equation like Y = -x is undefined or x^2 = -1 is undefined. We are never nervous when -5/0 or -1/0 arise for we say, undefined and ignore. But why be crazy when x^2 = -1 arises, and be naive and silly as to think i and -i are solutions.
So, this big picture guy would throw out the equation altogether.
And would ask, of only Positive Valued Equations or Polynomials, what is the pattern of solutions to those?
In Polynomials, only positive valued equations exist, and does that mean for each exponent of a positive valued polynomial have exactly N-1 solutions? Where N is exponent? Or, have just one and only one solution?
So, the real true blue question of Polynomial theory, was, you have a equation with a positive value solution. How many solutions per exponent?
AP

use a positive number with a minus sign in front of it, as if subtracting from zero, to indicate, say, a deficit.

[Ross A. Finlayson]

Post by Archimedes Plutonium
Newsgroups: sci.math
Date: Sun, 18 Jun 2017 22:23:11 -0700 (PDT)
Subject: we ignore A/0, why not ignore all negative numbers Re: may have found
how to get rid of negative numbers
Injection-Date: Mon, 19 Jun 2017 05:23:11 +0000
we ignore A/0, why not ignore all negative numbers Re: may have found how to get rid of negative numbers
- show quoted text -
Yes, excellent point from a idealist.
Is there negative money? Is there a negative gold coin. Is there a negative paper note to pay for -$1,112.
So what Chris is stumbling over and stumbling upon is his bad case of being brainwashed early in life and now fully accepts the brainwash, and wants to pass that brainwash off on others.
Do we really think a bank account is negative dollars?
Like the mother animal some billion years ago finding here young ones gone, missing, is using subtraction. But she is not saying there exists negative young.
So what do we call a missing bank amount? We call it not -$1,112. but rather call it deficit of $1,112.
Now it is easier to write the negative sign "-" than to write deficit, and so we do that convenience ploy. But we should never mistake negative signs as being something "genuine real".
We have let and allowed mathematicians to become philosophers foisting their stupid idealisms upon us and at the threat of failing us, if we dare tell them they are stupid in mathematics.
They were not stupid with A/0 where A is any Real number, positive Real number, and they realized it was undefined. But mathematicians were too stupid to confine negative numbers as also-- undefined.
Now, if you throw out negative numbers. Well then, you have no problems with sqrt-1. Because you never work with negative numbers-- you dispose of them as soon as they arise, just like you dispose of A/0.
So, now, since imaginary numbers can never arise, because you dispose of them. Why in the world have mathematicians spent over 5 centuries worried about a algebra that has solutions? Why were they worried that x^2 = -1 should have a solution? Why not just dispose of all equations like that, as saying, nonsense?
Well, we may say that those 5 centuries were wasted centuries, because mathematicians were too naive to ever look at the big picture-- if division has rooms of "thou shalt not touch" and subtraction is related to division, then subtraction has numbers to ignore as much as we ignore A/0.
The only place in science and wisdom that the negative numbers need be used, is in just a few select spots of science-- physics where you want a negative charge versus a positive charge, other than that, negative numbers are a utter waste of time.
AP
Newsgroups: sci.math
Date: Sun, 18 Jun 2017 22:58:58 -0700 (PDT)
Subject: Re: we ignore A/0, why not ignore all negative numbers Re: may have
found how to get rid of negative numbers
Injection-Date: Mon, 19 Jun 2017 05:58:58 +0000
Re: we ignore A/0, why not ignore all negative numbers Re: may have found how to get rid of negative numbers

Post by Archimedes Plutonium

Yes now, i believe this is a beautiful solution for negative numbers.
Rule of Negatives: whenever the final answer of a equation is a negative number it is undefined. Only positive number solutions exist.

Tell that to the bank.

Yes, excellent point from a idealist.
Is there negative money? Is there a negative gold coin. Is there a negative paper note to pay for -$1,112.
So what Chris is stumbling over and stumbling upon is his bad case of being brainwashed early in life and now fully accepts the brainwash, and wants to pass that brainwash off on others.
Do we really think a bank account is negative dollars?

Now think for a moment, if all mathematicians for the past 500 years had not all been naive, never looking at the big picture, always looking at the little chickenshat and spending time on shat.
What if there had been just one single mathematician in the past 500 years with his/her eyes on the big picture.
How much different would the Fundamental Theorem of Algebra, have been if we had a big picture guy in math.

Post by Archimedes Plutonium
Like the mother animal some billion years ago finding here young ones gone, missing, is using subtraction. But she is not saying there exists negative young.
So what do we call a missing bank amount? We call it not -$1,112. but rather call it deficit of $1,112.
Now it is easier to write the negative sign "-" than to write deficit, and so we do that convenience ploy. But we should never mistake negative signs as being something "genuine real".
We have let and allowed mathematicians to become philosophers foisting their stupid idealisms upon us and at the threat of failing us, if we dare tell them they are stupid in mathematics.

So if we had a big picture guy in the past 500 years in Algebra, would have said this-- we cannot use A/0 and call it undefined, that is the internal mechanics of mathematics. And, since division is intricately related to subtraction, means we have wholescale ignoring to do of negative numbers.
That is the Logic behind this. For A/0 is undefined and subtraction is related to division, hence vast amount of negatives are undefined.
And since we cannot be picky choosy on what negatives are undefined, we cannot see a individual negative, means we ignore all negatives. Until, or unless they are a use-- such as physics negative charge, but otherwise-- totally ignore them.

Post by Archimedes Plutonium
They were not stupid with A/0 where A is any Real number, positive Real number, and they realized it was undefined. But mathematicians were too stupid to confine negative numbers as also-- undefined.
Now, if you throw out negative numbers. Well then, you have no problems with sqrt-1. Because you never work with negative numbers-- you dispose of them as soon as they arise, just like you dispose of A/0.
So, now, since imaginary numbers can never arise, because you dispose of them. Why in the world have mathematicians spent over 5 centuries worried about a algebra that has solutions? Why were they worried that x^2 = -1 should have a solution? Why not just dispose of all equations like that, as saying, nonsense?

So, what would have the history of math been like if no-one bothered with FTA, herds of naive people quibbling over how many solutions for exponent 3?
What would a FTA look like where we obey the rule-- all negatives are undefined and are irrationals and infinites, just occupying Space, but useless to math.
What would a FTA look like under those circumstances?
I have a guess of what a pure true FTA would look like.

Post by Archimedes Plutonium
Well, we may say that those 5 centuries were wasted centuries, because mathematicians were too naive to ever look at the big picture-- if division has rooms of "thou shalt not touch" and subtraction is related to division, then subtraction has numbers to ignore as much as we ignore A/0.
The only place in science and wisdom that the negative numbers need be used, is in just a few select spots of science-- physics where you want a negative charge versus a positive charge, other than that, negative numbers are a utter waste of time.

I believe the pure and true FTA, where A/0 is undefined and no negative numbers arise, and if they do, they and the entire equation is undefined. So an equation like Y = -x is undefined or x^2 = -1 is undefined. We are never nervous when -5/0 or -1/0 arise for we say, undefined and ignore. But why be crazy when x^2 = -1 arises, and be naive and silly as to think i and -i are solutions.
So, this big picture guy would throw out the equation altogether.
And would ask, of only Positive Valued Equations or Polynomials, what is the pattern of solutions to those?
In Polynomials, only positive valued equations exist, and does that mean for each exponent of a positive valued polynomial have exactly N-1 solutions? Where N is exponent? Or, have just one and only one solution?
So, the real true blue question of Polynomial theory, was, you have a equation with a positive value solution. How many solutions per exponent?
AP

More fundamental theorems of algebra.