Theorem:: No Curves exist in math, and the Continuum is also nonexistent in math// Proof and comments

[Archimedes Plutonium]

Newsgroups: sci.math
Date: Wed, 28 Jun 2017 11:31:39 -0700 (PDT)

Subject: place this proof in the Math Array//Proof that No Curves exist and No
Continuum exists
From: Archimedes Plutonium <plutonium....@gmail.com>
Injection-Date: Wed, 28 Jun 2017 18:31:40 +0000


place this proof in the Math Array//Proof that No Curves exist and No Continuum exists

On Wednesday, June 28, 2017 at 12:33:22 AM UTC-5, alouatta....@gmail.com wrote:
(snipped)
>
> See what you can do with the fourth power.

Actually, it appears as though the higher the power, the more accurate the derivative and integral converges to the power rule without even having to go to higher Grids of 100 or 1000. For example at 5x^4, the integral and derivative come close to the Power Rule.

But, now, what I need to do especially is show that the GEOMETRY of the hinge at the midpoint produces all of calculus, and this can occur only if the derivative is itself part of the function graph as a straightline segment.

You cannot have a Calculus where the integral rectangle is a box with a curved top to the box, or, where the derivative is a curve segment.

The ability of the hinge box to be the Proof of the Fundamental Theorem of Calculus FTC, a geometry proof is ample warning enough, that Old Math Calculus with their Limit involved proof, is old decayed and invalid.

The below diagrams of a Calculus Chain, is ample proof that NO CURVE and NO CONTINUUM can exist in math, for it destroys the Calculus.

Calculus can only exist is Space as a coordinate system is DISCRETE with gaps and holes in between points of a function and points of the graph. Discrete Math rules all of mathematics. Shame I never took Discrete Math in school, even though I had ample opportunity. I should have taken it, instead I remember taking Differential Geometry, and learned little. My rebelliousness was apparent to me, even at the young age of 20, but it was rebelliousness, not learned, but rather, was already inside my mind that I had a steadfast notion of what math was good and what needed repair. Of course, at such a young age striving for grades, I was not about to rebell in class or to the teacher, for then, you had to conform. But a course in Discrete Math would have been good for I would have had at least some raw overview of Discrete Math.


diagrams of the chain x^5, 5x^4, 20x^3, 60x^2, 120x Re: no Curve, no Continuum exists in math, proving by a Calculus Chain

Preparing for tomorrow, and need to check for mistakes.

Tomorrow is here and found no mistakes, but now need to make abundantly clear.

This chain of derivatives (descending) and integrals (ascending) is a proof that no curves exist and no continuum exists. It means all of math is discrete with holes and gaps between Rationals. It means that no curve, even the circle is but tiny fine straightline regular polygons.

Now I need to check the below for errors, but what it shows is that the Calculus is all based upon a rectangle for integral area and a hinged right triangle, its hypotenuse for the derivative. It means the derivative is part of the starting function graph itself, and that a derivative of a tangent to a curve is poppycock nonsense.

function 120x
       132
        /|
      /  |
120/----|
  /      |
/        |
|        |
|        |
|        |
_____
.9  1  1.1


derivative of 120x as equal to 120 where dy/dx at x=.5 is 60/.5 = 120, and x=1 dy/dx = 120/1 = 120
       120
        /|
      /  |
 60/----|
  /      |
/        |
_____
0  .5  1


integral of 120x as box 1 * 60 as 60x^2 is 60 when x=1

______ 60
|         |
|         |
|         |
----------
0       1


xxxx
Alright, good, that first one was itself a straightline of Y = mx + b and all straightlines in calculus are going to be easy on derivative and integral. But notice, where few have ever noticed, that the integral of a Y = mx + b, pushes the starting function into being a curve of 2nd degree polynomial or function. So, here is the problem of Old Math-- do they ignore the fact that integral is a curve while the function itself is straightline and derivative is straightline. Ever since Leibniz and Newton, everyone just ignored this fact of mixing up straightlines and curves in Old Math. But I do not ignore it, and state further, that all of Calculus is just straightline segments. That the integral of 120x as 60x^2 is itself a bunch of tiny straightline segments 60(x)(x) where (x) is a straightline.
xxxx



function 60x^2
        72.6
        /|
      /  |
 60/----|
  /      |
/        |
|        |
|        |
|        |
_____
.9  1  1.1


derivative of 60x^2 as equal to 120x is dy/dx for x=.5 is 60/.5 = 120, and x=1 is 120/1 = 120

       120
        /|
      /  |
 60/----|
  /      |
/        |
_____
0  .5  1


integral of 60x^2 is 20x^3 as box .2 * 60 = 12 as 20x^3 interval .9 to 1.1 is 26.62 - 14.58 = about 12

______ 60
|         |
|         |
|         |
----------
.9       1.1


xxxx Now notice how cool the hinged box integral works, where you lift the box at midpoint, forming a trapezoid, and remember the trapezoid rule in Calculus? So the hinged box does not come from-- out of nowhere-- but is already a integral part of calculus. And all the more reason, that Calculus is all about tiny straightline segments. You cannot make the integral and derivative as INVERSES of one another, if you have to shift between being a "curve and being a straightline segment". The only way you can have derivative inverse integral, is if you work in only one medium-- all straightline segments.
xxxx


function 20x^3
       26.62
        /|
      /  |
 20/----|
  /      |
/        |
|        |
|        |
|        |
_____
.9  1  1.1     where x=.9, y= 14.58


derivative of 20x^3 as equal to 60x^2, but from function graph is dy/dx 6.62/.1 is approx 60 made better in 1000 Grid

       60
        /|
      /  |
  5 /----|
  /      |
/        |
_____
0  .5  1


integral of 20x^3 as box .2 * 20 = 4 as 5x^4 interval .9 to 1.1 as 7.32 - 3.28 = 4

______ 20
|         |
|         |
|         |
----------
.9       1.1


xxxx So, here in this CHAIN of Calculus of either ascending integrals or descending derivatives, we see that the Box calculus with its hinged midpoint solves every calculus problem. But in solving, it can only work if the derivative and integrals are all straightline segments, connecting Discrete points of a graph system, where there are holes and gaps in between. In Old Math, what they did, is play around with Limits, for they knew they had a problem of ever proving INVERSE in the FTC. They never had a notion that curves do not and cannot exist, so they came up with the goofy idea of playing around with Limits. To me, what the limit is like, is like hiring a seance telepathy person to make contact with the dead deceased and long buried people. The Limit voodoo dance.
xxxx


function 5x^4


       5
        /|
      /  |
.31 /----|
  /      |
/        |
_____
0  .5  1



derivative of 5x^4 as equal to 20x^3, but from function graph is dy/dx is 7.32-3.28 = 4 for dy and .2 for dx is 4/.2 is approx 20, and from formula is 20*1 = 20
 
       7.32
        /|
      /  |
  5/----|
  /      |
/        |
|        |
|        |
_____
.9  1  1.1     where x=.9, y= 3.28



integral of 5x^4 as box .2 * 5 = 1 as x^5 interval .9 to 1.1 as 1.61 - .59 = 1

______ 5
|         |
|         |
|         |
----------
.9       1.1

Alright, good, that CHAIN worked out fine. It is the content of a proof. A proof that mathematics has no Curve and has no Continuum. For if it had either one or both of those, then Math cannot have Calculus.

It is a picture proof of the Theorem Statement:: Math has no curve and no continuum, because math has a Calculus with a Fundamental Theorem of Calculus.

Proof Statement:: the above pictures is a proof. QED

AP

[Archimedes Plutonium]

Alright, I am satisfied that those pictures are a proof of no curves/ no continuum exists in math, otherwise we lose Calculus. That is a loss too large. Now I need to trim that proof, because the statement is far smaller than the proof. If I can do just one picture, then I have the proper proof for Conservation Principle of Math. So I define the CHAIN of integrals and refer to the chain in the proof.

Now a comment I made a few days ago is that the best proof of Math is a geometry argument. Now I wonder if that observation comes from human evolution that we evolved from apes throwing rocks and stones and where a brain evolves to "better throw" thus a evolution of a brain good with geometry in order to throw better. So, is the observation that a geometry proof is far better than a algebra proof, is that observation inside of math or is it due to our brains handling geometry better than handling algebra.

I am asking if math itself has a proof that geometry proofs are better than algebra proofs?

Aside from the fact that algebra is mostly abstract symbols whereas geometry is more about some substance of math, like drawing trapezoids and midpoints and right triangles in the No Curves Exist proof.

Quite frankly, I would say no, that algebra proofs and geometry proofs are equal in -- proving ability or capability. But then again, when we look at how much is unproven in algebra compared to geometry we see the mountain pile at algebra and not so much unproved conjectures on the geometry side.

The Atom Totality theory for which mathematics is but a tiny subset, would say that algebra and geometry are equals, no favoritism, and that our ease with geometry is a remnant of our evolution history.

But, however, if we look at the most mathematical part of physics-- EM theory, the AP-Maxwell Equations, do we get a sense that Geometry is larger than Algebra. The Old Physics Maxwell Equations, those 4 differential equations are mostly geometry, not algebra. So, in this sense, there maybe something to the idea that geometry proofs are the best proofs possible.

Another viewpoint is the history of mathematics, in that the first Logical system-- Euclid's Elements, is, afterall geometry, and axioms of geometry. Now for Algebra, a comparable system would have to wait until 1800s with Peano axioms for the Naturals, and covering only Naturals, whereas the Irrationals are still a mess. Number theory and ideas appear in Euclid, but just a add-on appendage.

CHAIN CALCULUS;; let me explore this some more. I feel more fruit is in this.

The chain I used was starting at x^5 and descending derivatives 5x^4, 20x^3, 60x^2, 120x, finally just 120. It is also a ascending integral.

In a certain sense, the CHAIN itself is a Calculus of a Calculus. A calculus upon calculus. It is as if the microscope put the microscope under the lenses. Or the telescope focusing upon its ownself.

x^5
5x^4
20x^3
60x^2
120x

Now if x = 1 we have the sequence for derivative as 1, 5, 20, 60, 120 as derivatives which, unexpectedly is increasing while the starting function is decreasing, and this is alarming.

And for the integrals we naturally expect a increasing integral area starting with 120x but instead, here again we are alarmed that the area decreases with starting function 120, 60, 20, 5, 1

So, what gives here? We would expect from our senses that starting with x^5 would have a larger derivative than 120x and that x^5 a larger integral area than 120x.

So our intuition is really battered by this. And instead of x=1, let us try x=2 or x=10. Now, when we use x=10, do we begin to get some normal behavior in this, for 10^5 is far larger than 1200.

Now, let me start a NEW CHAIN, instead of starting up at x^5, let me start a new Chain with just x, the identity function Y=x

x
1/2x^2
1/6x^3
1/24x^4
1/120x^5

That is a Chain of descending integral and ascending derivatives.

Now plugging in x=1 we have this progression for integrals 1, 1/2, 1/6, 1/24, 1/120

which, to my mind is bizarre for that should be the derivative getting smaller not the integral getting smaller

And now for the derivative sequence starting at 1/120x^5 is 1/120, 1/24, 1/6, 1/2, 1

which should be the integral not derivative sequence.

So, is the Chain somehow flipping around the integral and derivative?

And here again, if we put in x=2 or x=10 we reverse the situation to being more normal.

And, we have to ask, at what number, is a sort of midpoint in the Chains, to being normal?

Is it perhaps the number 2.71 for x or perhaps 3.14 for x so that the Chain acts normal again.

let me throw in x=3 to see if it begins to act normal

x^5 = 243
5x^4 = 405
20x^3 = 540
60x^2 = 540
120x = 360

Nope, no normal there, but normal with x=10

x^5 = 100000
5x^4 = 50000
20x^3 = 20000
60x^2 = 6000
120x = 1200

Normal there, but what is the number that it starts normal?

And what is the meaning of all of this?

AP

[Archimedes Plutonium]

On Wednesday, June 28, 2017 at 5:36:06 PM UTC-5, Archimedes Plutonium wrote:
(snipped)

>
> x^5 = 243
> 5x^4 = 405
> 20x^3 = 540
> 60x^2 = 540
> 120x = 360
>
> Nope, no normal there, but normal with x=10
>
> x^5 = 100000
> 5x^4 = 50000
> 20x^3 = 20000
> 60x^2 = 6000
> 120x = 1200
>

Alright, good, good, good, the thought occurred to me that the sequence above can be treated as one big Polynomial such as

x^5 + 5x^4 + 20x^3 + 60x^2 +120x

and I can throw in the derivative of 120x as 120

x^5 + 5x^4 + 20x^3 + 60x^2 +120x + 120

Now, if I bypass the leading coefficient of 1 and inspect the next coefficient of 5, then, is 5 the normalizing number? For x=5

x^5 = 3125
5x^4 = 3125
20x^3 = 2500
60x^2 = 1500
120x = 600

Now let me check with x^6 to see if 6 is the normalizing number x=6

x^6 = 46656
6x^5 = 46656
30x^4 = 38880
120x^3 = 25920
360x^2 =
720x =

Yes, I found the key to the normalizing number.

Now, a big new question arises, what is the meaning of a polynomial built from ascending integral or descending derivatives?

What does this polynomial mean for Calculus?

x^5 + 5x^4 + 20x^3 + 60x^2 +120x + 120

AP

[burs...@gmail.com]

Strange view on Peano. Peano had a formalist phase after he
published "Arithmetices principia, nova methodo exposita",
which culminated in "Formulario mathematico".

The later was translated in many languages and is a real
gem. There is a french edition and in this edition the
french word "racine" is used for root,

in both meanings, square root and root of a polynomial.
on page 110 he does quite a couple interesting satements
about racine based irrational numbers, old, from Euclid

and new, from Darboux etc.. So its quite unfair to reduce
peano to the few PA axios of natural numbers. At least together
with his colleges who helped him compile this gem,

it shows that he didn' stop at natural numbers. Some of
the cooler gems from this gem are:

page 176: pi 1000 digits
pi= 3.
14159 26535 89793 23846 26433 83279 50288 41971 69399 37510
58209 74944 59230 78164 06286 20899 86280 34825 34211 70679
82148 08651 32823 06647 09384 46095 50582 23172 53594 08128
etc...

page 177: cyclic numbers
e^(pi*i/12) = [sqrt(6)+sqrt(2)+i(sqrt(6)-sqrt(2))]/4
etc..

But you, AP, seem more to be interested in the derivative
of a function. Peano uses what I have already posted
(old hat algebra) for poloynomials p(z):

p(x) - p(y) is divisible x - y

he uses it as follows, and also allows non-polynomials f(z):

D f(x) := lim y->x ((f(x) - f(y))/(x-y))

he then quickly finds:

D x^n = n*x^(n-1)

This is all on page 138 ff. Have Fun:

Formulaire de Mathématiques
PUBLIÉ PAR G. PEANO
Professeur d'Analyse infinitésimale à l'Université de Turin

PARIS, GAUTHIER-VILLARS, IMPRIMEUR-LIBRAIRE
DU BUREAU DES LONGITUDES, DE L'ÉCOLE POLYTECHNIQUE,
Quai des Grands-Augustins, 55. 1901
http://ia902607.us.archive.org/24/items/formulairedesmat00pean/formulairedesmat00pean.pdf

[Archimedes Plutonium]

Now that polynomial was derived from the Power Rule of Calculus of a descending derivative starting with function x^5 or a ascending integral starting with 120 function Y = 120.

Now I see no connection to Calculus of ascent or descent if I happened to stumble on that polynomial and not knowing its background.

However, what if I considered derivatives as dy/dx, considered that division as subtraction and thus the polynomial of this:

x^5 - 5x^4 - 20x^3 - 60x^2 -120x - 120

Now, quickly I see that it would have a Positive Valued Zero Solution something in the range of say x=6.

More later,,,,

AP

[Archimedes Plutonium]

On Wednesday, June 28, 2017 at 8:34:44 PM UTC-5, Archimedes Plutonium wrote:
(snipped)
>

> x^5 - 5x^4 - 20x^3 - 60x^2 -120x - 120
>
> Now, quickly I see that it would have a Positive Valued Zero Solution something in the range of say x=6.
>

More like x=8, and have not yet pinned down the zero solution. It must be a factor of 120, and 10 is not it. But I think 8 is also too small. So, is this polynomial a contradiction to the Rational Coefficient theorem? Maybe I made a arithmetic error.

But, the minute after I posted my last I sensed a Spine Chilling Math theorem. A idea that knocks the socks off of every mathematician. That Geometry is primal to numbers to Algebra. You have to have geometry first, in order to next do algebra.

That is a spine chilling idea.

Where it comes from is that you cannot count first unless you have a geometry that is distinguishing a number of objects. And this gets into the argument of what is Abstraction and what is Objective Reality.

If we had a space of nothing, we have no geometry, and, we have no numbers.

If we had a Space of this object O we have a number 1 and if space had OO we have number 2.

Now, try to consider having number 1 and forming geometry. Try consider number 2 without geometry and then forming geometry from 2.

This is sounding like philosophy, until I do this::

Consider a atom, is it first geometry and then comes numbers, or, can we consider a atom as numbers then geometry?

So, we picture in our mind a Hydrogen atom as a ball and we see it as a geometry ball and now we picture this ball as 1. But it is composed of proton and electron so is this ball 1 or is it 2? The geometry says 1, the algebra says 2. But it is 1.

Still too much philosophy. And have to get rid of the philosophy to be science.

I am not denying algebra, but only asserting that geometry is more primal than algebra. The Maxwell Equations are on my side in this.

AP

[Archimedes Plutonium]

Yes, this can easily pass from philosophy musings into outright science. In fact feel i have a proof of it.

Theorem-statement:: Geometry is more primal than numbers (algebra). Meaning both and required to form mathematics, but that geometry came first and built numbers.

Proof statement:: physics has several complimentary concepts-- position to momentum, time to energy, but especially magnetism to electricity. And the magnetic field needs to come first to build electricity. QED

As a corollary of this theorem a geometry proof is always a superior proof.

AP

[Archimedes Plutonium]

On Wednesday, June 28, 2017 at 9:08:11 PM UTC-5, Archimedes Plutonium wrote:
> On Wednesday, June 28, 2017 at 8:34:44 PM UTC-5, Archimedes Plutonium wrote:
> (snipped)
> >
> > x^5 - 5x^4 - 20x^3 - 60x^2 -120x - 120
> >
> > Now, quickly I see that it would have a Positive Valued Zero Solution something in the range of say x=6.
> >
>
> More like x=8, and have not yet pinned down the zero solution. It must be a factor of 120, and 10 is not it. But I think 8 is also too small. So, is this polynomial a contradiction to the Rational Coefficient theorem? Maybe I made a arithmetic error.
>

In College Algebra by Stewart, Redlin, Watson, 2004, page 333, they call it the Rational Zeros Theorem which basically says the the Leading coefficient together with the Ending coefficient permutations of the factors is all the possible rational zero solutions.

Well, the factors of 120 are two of them are 8 and 10, but I know of none in between.

So I try 8 and it is too small, so I try 8.5 and it is a bit too large. So somewhere between 8 and 8.5 is a zero solution.

Either I made a arithmetic error or, the Rational Zeros Theorem is not universally true.

AP

[Archimedes Plutonium]

I think this problem happened to me once in the past with the Rational Zeroes Theorem in that the theorem is poorly worded. Poorly worded and needs to include this phrase to make it clear. Stewart, Redlin, and Watson failed on making this theorem clear--

If a polynomial in New Math has a zero solution, it can either be rational or irrational, but if it is rational then it must be a factor permutation of leading and ending coefficients.

I remember back years ago when this theorem caused a mess and Peter Percival chimed in and pointed out the flub up.

I blame it on poor writing of theorems.

AP

[Archimedes Plutonium]

Just like in physics, math is complimentary duals

Position versus Momentum

Time versus Energy

Magnetism versus Electricity

For math it is

Geometry versus Algebra (numbers)

Now do not mistake complimentarity in that both are needed but one is more primary, more fundamental than the other.

For math it is geometry, and that makes a geometry proof of an item superior to a algebra proof.

AP

[Archimedes Plutonium]

On Thursday, June 29, 2017 at 12:02:31 AM UTC-5, Archimedes Plutonium wrote:
> On Wednesday, June 28, 2017 at 9:08:11 PM UTC-5, Archimedes Plutonium wrote:
> > On Wednesday, June 28, 2017 at 8:34:44 PM UTC-5, Archimedes Plutonium wrote:
> > (snipped)
> > >
> > > x^5 - 5x^4 - 20x^3 - 60x^2 -120x - 120
> > >
> > > Now, quickly I see that it would have a Positive Valued Zero Solution something in the range of say x=6.
> > >

No I am not an insomniac, in fact I get more than 8 hrs sleep per day, sometimes even 12 hrs. I take a lot of naps, and find myself late at night able to do more work because I am not bothered by any distractions.

Now, by the way, let me report on the horticulture of the rock elm, cherry, yew, currant cuttings. The only ones to survive were the yew and the currants. I thought the blackberries would survive but maybe it got too wet. I was hoping for the Rock Elm, but they are difficult to cutting root propagation. So I planted about 15 yews for a hedge and about 4 currants. I love currants.

Before heading off to bed I need to post what is on my mind about the Chain Calculus.

x^5 - 5x^4 - 20x^3 - 60x^2 -120x - 120

that polynomial has a irrational solution of about 8.5

Now breaking that equation down further

5x^4 -20x^3 -60x^2 -120x -120 has a irrational solution approx 5.9

20x^3 -60x^2 -120x -120 has another irrational solution approx 4.5

60x^2 -120x -120 has irrational solution of about 2.7

120x -120 has a rational solution of 1

Now, unless I am so groggy I believe there is a easy proof and theorem that basically says every Y = mx +b where m and b are rationals has a Y intercept and a X intercept if such exists as Rational number solutions. In other words, cannot have an irrational number solution. Correct me if wrong for I am a bit groggy.

So, now, in New Math, since we connect via straightline segments from point P_1 to P_2, would mean that all X-intercepts of the above polynomials would be Rational solutions, not irrational.

Since curves do not exist in New Math, then all Polynomials, no matter the degree, have only x and y intercepts that are Rational number solutions.

So in the polynomials above, instead of irrational approx 5.9, in each Grid, whether 10, 100, 1000 we lop off the irrational approximation and have as our answer a Rational Number solution such as 5.9.

Now I need to work on having all functions in the 1st Quadrant Only and truncating any part of the function that lies in the other three quadrants.

Having mathematics focus on just plain first quadrant only and all the other quadrants are pure distraction baloney, not needed.

Now if you want a parabola or a full hyperbola, you can scoot them over into the 1st Quadrant Only and then wrestle with their transformation. The trouble with negative numbers, is simply, they do not exist and then, they interfer with what the answer really should be.

Now physics has and had a similar problem, where infinities kept interfering with what the truth was. It is called Renormalization in Quantum Electrodynamics. Trouble is that math came to this sweeping new understanding far too late, but is just now beginning to do the same. Remove all negatives all imaginaries and all complex numbers, as fictional imagination run amok.

AP

[burs...@gmail.com]

Do we really need derivative? Here on page 75, the author
uses talyor expansion and hence derivative of polynomials
to show that polynomials are continuous.

First Course in the Theory of Equations
Leonard Eugene Dickson
https://www.gutenberg.org/files/29785/29785-pdf.pdf

Lets give it a try without derivatives, we have already
seen the old hat of algerba:

p(x) - p(y) divisible by x - y

Or more precisely:

(p(x) - p(y)) / (x - y) = q(x,y)

with q one degree less than p. Now lets see what happens
in the vincinity of a, we have:

(p(a+h) - p(a)) / (a+h - a) = q(a+h,a)

Which can be transformed into:

p(a+h) = p(a) + h*q(a+h,a)

The h*q(a+h,a) is the F of Dickson, and could be obtained
by an even more simpler method, just formally compute
p(a+h)-p(a), but lets continue with the main argument here,

namely that p is continuous around a, i.e. has no jumps.
for this purpose we look at h*q(a+h,a), it will read:

h*q(a+h,a) = a_1*h + a_2*h^2 + ... + a_n*h^n

= F

Note a_i are not the coefficients of p, instead just
the coefficients of the F of Dickson. Let:

g = max(|a_1|,..,|a_n|)

We see that for h<1:

|F| < g*(h + h^2 + ... + h^n)

< g*h/(1-h) /* geometric series */

So if we ask whether:

|F| < p

We get the answer yes, for:

h < p/(p+g)

So no jumps.

[Don Redmond]

A is like B, D is like E. Therefore geometry beats numbers.

This is a proof?????


Don

[Don Redmond]

I think this got explained to you a long time ago. Just because a polynomial has rational coefficients does not mean it has rational zeros. Take x^2 - 2 = 0.
Rational coefficients no rational (at least in old math) zeros.

All the rational zeros theorem is about is possible rational zeros. It does not say there are rational zeros.

Don

[Archimedes Plutonium]

Now if I take a cutting of a willow, I am almost 99% going to get a plant, from root cutting propagation.

But why is an elm so darn difficult.

I suppose researchers can find into the genetics of plants, why some are so difficult and others so easy.

AP

[Archimedes Plutonium]

On Thursday, June 29, 2017 at 2:26:31 PM UTC-5, Don Redmond wrote:
(snipped)

>
> A is like B, D is like E. Therefore geometry beats numbers.
>
> This is a proof?????
>
>
> Don

Some years back, Don, you accused me of putting words in your mouth. Is not your above the ultimate in words in mouth.

Let me be Socrates, and you Don, be Don Redmond.

Soc:: you know geometry and algebra are different, G and A but complimentary

DR:: G is like A

Soc:: No, different yet complimentary, for complimentary means necessary but different

DR:: I never took physics

Soc:: that's okay, for position and momentum are complimentary just like Geometry and Algebra are complimentary

DR:: Oh, yes, now I remember, like time and energy are complimentary, different but needed

Soc:: yes, now you got the hang of it, and the most important complimentary of all is magnetism with electricity, because all the other complimentaries are contained in magnetism and electricity, even mathematics of geometry and algebra are inside of magnetism with electricity

DR:: that is news to me, you teaching an old dog new tricks, want a bisquit?

Soc:: so now, let's get to work, position is different from momentum, but you need one of them to appear in creation first, you cannot have the first to be is momentum because that precludes position. Likewise time and energy, one has to be in creation first for you cannot have energy before you have time since time is a part of energy. Likewise, you cannot have electricity before you have magnetism, because magnetism is a part of electricity. All Complimentary Relationships need a "first element".

DR:: my physics is rusty, but I follow the argument

Soc:: So, math is a compliment of Geometry and Numbers, both are different yet needed to make math. And as in all Compliments, one has to come first, precede the other. Which comes first, Geometry or shape or form or design? Does Geometry form come first, or does Number quantity, algebra, counting come first.

DR:: yes indeed that rings bells, I forgot what religion said "And first there was Form and from the Form came a number of life... was it Apollo and Zeus?

Soc:: Good, you learned something today Mr. Don Redmond, you learned that Form, which is geometry, comes first, came first, and only afterwards comes numbers and counting.

DR:: time for a bisquit, (in German, cookie)?

AP

[Archimedes Plutonium]

On Thursday, June 29, 2017 at 2:30:55 PM UTC-5, Don Redmond wrote:
(snipped)
>

> I think this got explained to you a long time ago. Just because a polynomial has rational coefficients does not mean it has rational zeros. Take x^2 - 2 = 0.
> Rational coefficients no rational (at least in old math) zeros.
>
> All the rational zeros theorem is about is possible rational zeros. It does not say there are rational zeros.
>
> Don

It only recently got explained to you Don that an irrational number is not a single solo number.

All Rationals are single solo numbers.

Your irrational sqrt2 is actually two different numbers acting as one number so that sqrt2 is both 1.414 and 1.415 in 1000 Grid.

So, Don, you keep failing the lessons taught you. If you have a polynomial x^2 -2 then you claim the solution is sqrt2, which means both 1.414 and 1.415 in 1000 grid, and 1.41 with 1.42 in 100 Grid.

So, Don, your solution as irrational has no fixed number but is constantly vibrating between different rational numbers.

You seem never capable of grasping the idea that a number should be FIXED, not wavering between different numbers.

So, in Polynomial theory, depending on what Grid you are in, the polynomial x^2 -2 has only Rational solutions and in 1000 Grid, you have a choice of whether you select 1.414 or you select 1.415 as your rational solution. And this is in agreement with the idea that x^2 -2 is not a curve but a chain of tiny straightline segments.

You undoubtedly know and agree that all Y=mx + b with rational m and b have all X-intercepts being Rationals. You know that.

So when x^2 -2 is a chain of Y=mx+b, when that chain of straightline segments crosses the X axis, you have a Rational number solution, not irrational.

Drink a beer on that Don, and call me in the morning.

AP

[Chris M. Thomasson]

On 6/29/2017 2:18 PM, Archimedes Plutonium wrote:
> On Thursday, June 29, 2017 at 2:30:55 PM UTC-5, Don Redmond wrote:
> (snipped)
>>
>> I think this got explained to you a long time ago. Just because a polynomial has rational coefficients does not mean it has rational zeros. Take x^2 - 2 = 0.
>> Rational coefficients no rational (at least in old math) zeros.
>>
>> All the rational zeros theorem is about is possible rational zeros. It does not say there are rational zeros.
>>
>> Don
>
> It only recently got explained to you Don that an irrational number is not a single solo number.
>
> All Rationals are single solo numbers.
>
> Your irrational sqrt2 is actually two different numbers acting as one number so that sqrt2 is both 1.414 and 1.415 in 1000 Grid.

Wrt arbitrary precision, any irrational number with a given precision
level can be expressed as two integers a and b such that a/b recreates
the irrational up to said precision. Look up convergents of continued
fractions.
[...]

[j4n bur53]

AP is assuming a grid, a very large one, it can be up
to 10^604. And its an affine plane, and not the surface
of a sphere. This is all very inconsequental.

Already having sqrt2 to such a high precision such as
between 1.414 and 1.415 is not realistic. All we would
need is sqrt2 between 1.4 and 1.5.

The situtation is different if the argument is larger,
sqrt200, we would then have a twin number and not
anymore a solo number between 14.1 and 14.2.

But since we are on a sphere, sqrt200 might vary
considerable. Its not a vibrating, but since sqrt200
is much bigger than sqrt2,

this is only the natural latitude dependency, everything
close to the north pole or close to the south poly is
smaller than close to the äquator,

this is because earth is not ellipsoid, but more precisely
and ovaloid, which is also reflected in the oval conic
sections discovered by AP.

So basically in new math, there would be very many values
of sqrt200, depending on the maidenhead locator where we
horticulturally take the square root sqrt200.

Chris M. Thomasson schrieb:

[burs...@gmail.com]

So, Don, new math is clearly superior to old math,
because geometry comes first. But now I have to
take a piss, and then continue watching

Sesame Street on my electronic tube TV. Thats all
I do day in and day out, if I am not spamming sci.math.
And since my last seizure fully sleeping

is also not anymore impossible for me. So every
night I am half awake and do watch Sesame Street.

[Archimedes Plutonium]

Chris, you disappoint me. You came so close, so very close, just a millimeter away from saying the irrational number is two numbers, not one solo number. THAT IS WHY irrationals are irrational, because two rationals have to compose them.

You disappoint Chris, and is this how all polluted minds work, Chris. That they come up to the edge of the Ocean of Knowledge== irrational is two rationals, but then, never realize what they should realize.

Chris, when you got married, did you get so close to your wife, but when you were a millimeter away, that you never went any further?

I mean, talk about math naivety or as the French would say naivete

Talk about being dense, or as the German's would say, der dense

You made it there Chris, to the creeks edge-- now go in

You made it there to the rivers edge-- now go in

You made it there to the ocean's edge-- now go in

Irrational numbers are vibrating numbers because they are not a single solo number. Irrational numbers are at least, at least, at least two different Rationals, but often are more than two different rationals.

The reason Math has to be a Grid System, is because Rationals are the Grid points and the empty space between the Rationals are irrationals.

For Calculus to exist, it needs straightlines connecting every point of the function graph, and in between those points are irrationals as empty space.

You cannot work with irrationals in math because-- which of the rationals do you pick, do you pick 1.41 or 1.42 or 1.414 or 1.415. Math is precision, and when your number vibrates between being several different rationals, then you have no mathematical answer.

What is the solution for x^2 -2 = 0, what is that solution Chris, or Don?

You have been taught and scolded in school to come up with the answer sqrt2.

In truth, that is a false answer, because in true math, sqrt2 is many different numbers.

If you had come up with the answer that the solution of x^2 - 2 = 0 is 1.414 with 1.415 in 1000 Grid where both are rational numbers, you would have thence given the correct answer.

All solutions, in mathematics, have to be a Rational Number. Irrationals exist only as a place-marker that make up empty space.

Disappointed in you Chris, you came so close, yet still so far away. Get an organic beer on me.

AP

[Chris M. Thomasson]

On 6/29/2017 4:56 PM, Archimedes Plutonium wrote:
> On Thursday, June 29, 2017 at 4:23:30 PM UTC-5, Chris M. Thomasson wrote:
>> On 6/29/2017 2:18 PM, Archimedes Plutonium wrote:
>>> On Thursday, June 29, 2017 at 2:30:55 PM UTC-5, Don Redmond wrote:
>>> (snipped)
>>>>
>>>> I think this got explained to you a long time ago. Just because a polynomial has rational coefficients does not mean it has rational zeros. Take x^2 - 2 = 0.
>>>> Rational coefficients no rational (at least in old math) zeros.
>>>>
>>>> All the rational zeros theorem is about is possible rational zeros. It does not say there are rational zeros.
>>>>
>>>> Don
>>>
>>> It only recently got explained to you Don that an irrational number is not a single solo number.
>>>
>>> All Rationals are single solo numbers.
>>>
>>> Your irrational sqrt2 is actually two different numbers acting as one number so that sqrt2 is both 1.414 and 1.415 in 1000 Grid.
>>
>> Wrt arbitrary precision, any irrational number with a given precision
>> level can be expressed as two integers a and b such that a/b recreates
>> the irrational up to said precision. Look up convergents of continued
>> fractions.
>> [...]
>
> Chris, you disappoint me. You came so close, so very close, just a millimeter away
> from saying the irrational number is two numbers, not one solo number. THAT IS WHY > irrationals are irrational, because two rationals have to compose them.

[...]

You totally missed my point. Oh well. Have a nice day!

:^)

[Archimedes Plutonium]

No i get your point very well Chris, very well, that you live in a Newton Bubble of Absolute Time Space and Knowledge and that whenever you see someone differing from your bubble point of view you say they -- don't get it

Did it occur to you that someone can be smarter than you, and you are the one deficient in understanding.

Maybe bubbles not only corrupt, but corrupt absolutely

[Chris M. Thomasson]

Blah.

[burs...@gmail.com]

Apropos time and space, 10^604 is too much and not spherical,
so it must be instead the maidenhead locator, everything else

is corrupting physical reality by imaginary bubbles. BTW: AP you
could also entertain us by putting a fruit hat on your head,

and singing your song of bananas is your business:

Carmen Miranda - Tico-Tico No Fubá
https://www.youtube.com/watch?v=bioGCIPKuiM

[Archimedes Plutonium]

On Wednesday, June 28, 2017 at 1:42:56 PM UTC-5, Archimedes Plutonium wrote:
> Newsgroups: sci.math
> Date: Wed, 28 Jun 2017 11:31:39 -0700 (PDT)
>
> Subject: place this proof in the Math Array//Proof that No Curves exist and No
> Continuum exists
> From: Archimedes Plutonium <plutonium....@gmail.com>
> Injection-Date: Wed, 28 Jun 2017 18:31:40 +0000
>

Alright, a lot of horrible errors on my part, alot.

So I redid the entire post:


place this proof in the Math Array//Proof that No Curves exist and No Continuum exists

On Wednesday, June 28, 2017 at 12:33:22 AM UTC-5, alouatta....@gmail.com wrote:
(snipped)
>
> See what you can do with the fourth power.

Actually, it appears as though the higher the power, the more accurate the derivative and integral converges to the power rule without even having to go to higher Grids of 100 or 1000. For example at 5x^4, the integral and derivative come close to the Power Rule.

But, now, what I need to do especially is show that the GEOMETRY of the hinge at the midpoint produces all of calculus, and this can occur only if the derivative is itself part of the function graph as a straightline segment.

You cannot have a Calculus where the integral rectangle is a box with a curved top to the box, or, where the derivative is a curve segment.

The ability of the hinge box to be the Proof of the Fundamental Theorem of Calculus FTC, a geometry proof is ample warning enough, that Old Math Calculus with their Limit involved proof, is old decayed and invalid.

The below diagrams of a Calculus Chain, is ample proof that NO CURVE and NO CONTINUUM can exist in math, for it destroys the Calculus.

Calculus can only exist is Space as a coordinate system is DISCRETE with gaps and holes in between points of a function and points of the graph. Discrete Math rules all of mathematics. Shame I never took Discrete Math in school, even though I had ample opportunity. I should have taken it, instead I remember taking Differential Geometry, and learned little. My rebelliousness was apparent to me, even at the young age of 20, but it was rebelliousness, not learned, but rather, was already inside my mind that I had a steadfast notion of what math was good and what needed repair. Of course, at such a young age striving for grades, I was not about to rebell in class or to the teacher, for then, you had to conform. But a course in Discrete Math would have been good for I would have had at least some raw overview of Discrete Math.


diagrams of the chain x^5, 5x^4, 20x^3, 60x^2, 120x Re: no Curve, no Continuum exists in math, proving by a Calculus Chain

Preparing for tomorrow, and need to check for mistakes.

Tomorrow is here and found no mistakes, but now need to make abundantly clear.

This chain of derivatives (descending) and integrals (ascending) is a proof that no curves exist and no continuum exists. It means all of math is discrete with holes and gaps between Rationals. It means that no curve, even the circle is but tiny fine straightline regular polygons.

Now I need to check the below for errors, but what it shows is that the Calculus is all based upon a rectangle for integral area and a hinged right triangle, its hypotenuse for the derivative. It means the derivative is part of the starting function graph itself, and that a derivative of a tangent to a curve is poppycock nonsense.

starting function 120x

       132
        /|
      /  |
120/----|
  /      |
/        |
|        |
|        |
|        |
_____
.9  1  1.1


derivative of 120x as equal to 120 via Power Rule, but, where dy/dx is concerned we have 12/.1 = 120

integral of 120x as box .1 *120 is 12 and as Power Rule is 60x^2 giving us
72.6 - 60 is approx 12.

______ 120
|         |
|         |
|         |
----------
1       1.1


xxxx
Alright, good, that first one was itself a straightline of Y = mx + b and all straightlines in calculus are going to be easy on derivative and integral. But notice, where few have ever noticed, that the integral of a Y = mx + b, pushes the starting function into being a curve of 2nd degree polynomial or function. So, here is the problem of Old Math-- do they ignore the fact that integral is a curve while the function itself is straightline and derivative is straightline. Ever since Leibniz and Newton, everyone just ignored this fact of mixing up straightlines and curves in Old Math. But I do not ignore it, and state further, that all of Calculus is just straightline segments. That the integral of 120x as 60x^2 is itself a bunch of tiny straightline segments 60(x)(x) where (x) is a straightline.
xxxx



starting function 60x^2

        72.6
        /|
      /  |
 60/----|
  /      |
/        |
|        |
|        |
|        |
_____
.9  1  1.1


derivative of 60x^2 as equal to 120x and is 120 when x+1 in Power Rule but is dy/dx for x=1 is 12.6/.1 which is almost 120

integral of 60x^2 is 20x^3 as box .2 * 60 = 12 as 20x^3 interval .9 to 1.1 is 26.62 - 14.58 = about 12 and made better in 1000 Grid

______ 60
|         |
|         |
|         |
----------
.9       1.1


xxxx Now notice how cool the hinged box integral works, where you lift the box at midpoint, forming a trapezoid, and remember the trapezoid rule in Calculus? So the hinged box does not come from-- out of nowhere-- but is already a integral part of calculus. And all the more reason, that Calculus is all about tiny straightline segments. You cannot make the integral and derivative as INVERSES of one another, if you have to shift between being a "curve and being a straightline segment". The only way you can have derivative inverse integral, is if you work in only one medium-- all straightline segments.
xxxx


starting function 20x^3

       26.62
        /|
      /  |
 20/----|
  /      |
/        |
|        |
|        |
|        |
_____
.9  1  1.1     where x=.9, y= 14.58


derivative of 20x^3 is equal to 60x^2 in Power Rule and for x= 1 is 60, but from function graph is dy/dx 6.62/.1 is approx 60 made better in 1000 Grid


integral of 20x^3 as box .2 * 20 = 4 as 5x^4 interval .9 to 1.1 as 7.32 - 3.28 = 4

______ 20
|         |
|         |
|         |
----------
.9       1.1


xxxx So, here in this CHAIN of Calculus of either ascending integrals or descending derivatives, we see that the Box calculus with its hinged midpoint solves every calculus problem. But in solving, it can only work if the derivative and integrals are all straightline segments, connecting Discrete points of a graph system, where there are holes and gaps in between. In Old Math, what they did, is play around with Limits, for they knew they had a problem of ever proving INVERSE in the FTC. They never had a notion that curves do not and cannot exist, so they came up with the goofy idea of playing around with Limits. To me, what the limit is like, is like hiring a seance telepathy person to make contact with the dead deceased and long buried people. The Limit voodoo dance.
xxxx


function 5x^4

       7.32
        /|
      /  |
  5/----|
  /      |
/        |
|        |
|        |
_____
.9  1  1.1     where x=.9, y= 3.28

derivative of 5x^4 as equal to 20x^3 in Power Rule is 20, but from function graph is dy/dx is 7.32-3.28 = 4 for dy and .2 for dx is 4/.2 is 20, both matching in value
 

integral of 5x^4 as box .2 * 5 = 1 as x^5 interval .9 to 1.1 as 1.61 - .59 = 1

______ 5
|         |
|         |
|         |
----------
.9       1.1

Alright, good, that CHAIN worked out fine. It is the content of a proof. A proof that mathematics has no Curve and has no Continuum. For if it had either one or both of those, then Math cannot have Calculus.

It is a picture proof of the Theorem Statement:: Math has no curve and no continuum, because math has a Calculus with a Fundamental Theorem of Calculus.

Proof Statement:: the above pictures is a proof. QED

AP

[Julio Di Egidio]

On Friday, June 30, 2017 at 2:32:48 AM UTC+2, Chris M. Thomasson wrote:
> On 6/29/2017 4:56 PM, Archimedes Plutonium wrote:
> > On Thursday, June 29, 2017 at 4:23:30 PM UTC-5, Chris M. Thomasson wrote:
> >> On 6/29/2017 2:18 PM, Archimedes Plutonium wrote:
> >>> On Thursday, June 29, 2017 at 2:30:55 PM UTC-5, Don Redmond wrote:
> >>> (snipped)
> >>>>
> >>>> I think this got explained to you a long time ago. Just because a polynomial has rational coefficients does not mean it has rational zeros. Take x^2 - 2 = 0.
> >>>> Rational coefficients no rational (at least in old math) zeros.
> >>>>
> >>>> All the rational zeros theorem is about is possible rational zeros. It does not say there are rational zeros.
> >>>

> >>> It only recently got explained to you Don that an irrational number is not a single solo number.
> >>>
> >>> All Rationals are single solo numbers.
> >>>
> >>> Your irrational sqrt2 is actually two different numbers acting as one number so that sqrt2 is both 1.414 and 1.415 in 1000 Grid.
> >>
> >> Wrt arbitrary precision, any irrational number with a given precision
> >> level can be expressed as two integers a and b such that a/b recreates
> >> the irrational up to said precision. Look up convergents of continued
> >> fractions.
> >> [...]
> >
> > Chris, you disappoint me. You came so close, so very close, just a millimeter away
> > from saying the irrational number is two numbers, not one solo number. THAT IS WHY > irrationals are irrational, because two rationals have to compose them.
> [...]
>
> You totally missed my point. Oh well. Have a nice day!

No, he is totally correct: that in fact exists (*) as mathematics of the
finite and it does have guaranteed correctness, based on the so called
containment constraint, i.e. that all solutions are guaranteed to be
bounded by the returned interval, and the quality of an implementation
is in the sharpness of the interval: it's standard mathematics that
really is broken...

(*) The reference book is this one:
<https://books.google.it/books?id=tY2wAkb-zLcC&lpg=PR3&ots=IiGVRs0ipP&dq=global%20optimization%20using%20interval%20analysis&lr&pg=PR3#v=onepage&q=global%20optimization%20using%20interval%20analysis> Note that, despite the title, the book contains the full development,
from arithmetic to analysis.

Have fun,

Julio

[burs...@gmail.com]

And how do you define your correctness criteria? Where
do you take the "solutions" from, and that they are "contained"
in the interval? Out of your ass?

[Archimedes Plutonium]

Thanks Julio, two questions please. Is there a real nice textbook on Finite Mathematics, one comparable as what the Stewart Calculus book is to calculus-- written by someone interested in teaching calculus. I made the mistake in the 1990s of buying books on p-adics, and now see that it was a total waste of time. I want to see if anyone in mathematics has pushed the idea that the Cartesian Coordinate System needs a total revamp, and where all of mathematics functions, graphs are in a Grid of Rational Points, 1st Quadrant Only. Is there such a book on Finite Math-- perhaps it will be my last course of math.

Second question, please, am I the only mathematician that is adamant of getting rid of all negative numbers and Graphing in 1st Quadrant Only. Is there another mathematician on that same program?

AP

[burs...@gmail.com]

Thanks dear God, that I am not born brain amputated.

[Chris M. Thomasson]

Thank you for that.

[Chris M. Thomasson]

Wrt my comment about using two integers to represent a given precision
of an irrational, well, its correct up to that given precision. We
cannot gain two finite integers to represent an infinite irrational.

[Chris M. Thomasson]

Fwiw, for instance, if somebody said they need two integers to represent
4 digits of pi, including the leading 3, to fit their personal needs, well:

512 / 163 does the trick.

That's all they need, and these integers do the trick.

[burs...@gmail.com]

Other "representations" of some irrational numbers, work
with integers only. For example polynomials:

p(z) = a0+a1*z+..+an*z^n

They need only the information of the integers <a0,a1,..,an>
and they represent all the algebraic numbers.

And this representation is exact.

[burs...@gmail.com]

Using only the positive quadrant, is rather trivial.
This would mean we would only consider positive algebraic

numbers. For an algebraic number b1>0, and the other
roots b2,..,bn>0 the polynomial will be:

p(z) = (z-b1)*(z-b2)*..*(z-bn)

What you cannot guarantee is that p(z) is always positive
for all z. Lets assume the roots are ordered b1 < b2 < ..
< bn, and they are all distinct, so the polynomial is square free.

What does the curve do? Well if p(z) < 0 for z < b1, then
the curve will do (if p(z) > 0 for z < b1, then use
opposite signs):

- b1 + b2 - + .. bn +/-

Proof: By induction, the base case p(z) = z-b1 is trivial,
this curve is a straight 45% degree line, which crosses
the x-axis at b1, so we have this picture:

- b1 +

the step case, let p(z) = (z-b1)*q(z). Lets only look
at the case where q(z) < 0 for z < b2 for the moment.
So we have for the polynomial q(z) by induction hypothesis:

- b2 - + .. bn +/-

Now since z-b1>=0 for z>=b1 we see that we have
as a result for the polynomial p(z):

b1 - b2 + - .. bn +/-

And since z-b1<0 for z<b1 we see that we have as a
result for the polynomial p(z):

+ b1

If we put the two together we get as result for the
polynomial p(z), as required:

+ b1 - b2 + - .. bn +/-

So basically if q(z) < 0 for z < b2, then p(z) > 0 for
z < b1. The other case can be similarly derived, if
q(z) > 0 for z < b2, the p(z) < 0 for z < b1.

The above pattern also shows that p(z) >= 0 for z >= 0
is only possible if n=1 and b1=0, its only possible for:

p(z) = z

all other polynomials with positive roots will do the
chicken dance.

[burs...@gmail.com]

Corr.:

So we have for the polynomial q(z) by induction hypothesis:

- b2 + .. bn +/-

[Archimedes Plutonium]

On Friday, June 30, 2017 at 1:53:22 PM UTC-5, Chris M. Thomasson wrote:

>
> Fwiw, for instance, if somebody said they need two integers to represent
> 4 digits of pi, including the leading 3, to fit their personal needs, well:
>
> 512 / 163 does the trick.
>
> That's all they need, and these integers do the trick.

And that is the whole point of the idea-- every irrational number is two rationals that compose the irrational number.

So the world has only Rationals that exist.

A rational is a single fixed solo number.

A irrational is not a solo number but composed of two or more different rationals.

The sqrt2 in 100 Grid is 1.41 with 1.42, and in 1000 Grid is 1.414 with 1.415.

Now the irrational pi is different from sqrt2 or sqrt3 or sqrt5 etc etc because it is two rationals in division rather than multiplication. In 10 Grid, pi is 19/6 as 3.1, then it is 22/7 for 3.14 etc

The "e" number is also irrational divisional number in 10 Grid 11/4 is 2.7, in 100 Grid 19/7 is 2.71 etc etc

Most irrationals are multiplication of two rationals, some irrationals (thought of as transcendental appear to all be division irrationals-- need a proof here).

But the real big point and message in all of this, is what glides over the head of Chris, constantly gliding over his head, for he is blinded with his stupid idea of infinity that tangles up his mind.

The big point is that Rationals are FIXED SOLO NUMBERS, while Irrationals require TWO DIFFERENT RATIONALS to compose them. Thus, irrationals are not fixed, but vibrating back and forth between different numbers.

It is like markers, and you have rocks as markers and you have two persons dancing as a marker. So that a triangle of 1-1-sqrt2 would look like this, where the 1 is a rock and the || is two people dancing::


||

1 1

And the angles are 90, irrational 45, rational 45.

Julio understands this, but for some reason, Chris is blinded to the idea, that what it means to be Rational is it means FIXED SOLO NUMBER, and irrational means TWO DIFFERENT Rationals VIBRATING and acting as one number.

Now I do not know if the globalization work Julio is pointing out is proof that an irrational is two different vibrating Rationals.

All I can say on this issue is that a proof should be easy to render-- in the fact that for numbers multiplied for a square root like 2, that the irrational of one and the same number 1.414213.... that multiplying that same number never reaches 2.0000.... or ever bounces back and forth between say 1.999.... and say 2.0000... or 2.0000..1. The pinnacle of Old Math on sqrt2 is always 1.999... never able to reach 2.000... And of course, Old Math has screwballs who constantly say 1.999... is 2.000... only because they are not logical but screwballs.

Whereas, you instantly see a bouncing back and forth with TWO DIFFERENT NUMBERS USED 1.414 x 1.414 is 1.999.. while 1.414 x 1.415 = 2.000... So a simple proof is that multiplication of IDENTICAL SAME NUMBER never yields a 2.0000.... Whereas multiplication by Different Numbers always gets you the 2.0000....

But recently I asked that PHYSICS look into mathematics with its LIGO machine of precision lasers. Where it can actually measure a 45-45-90 Right Triangle and see if it can determine if the one angle is VIBRATING, or if the distance is 1, 1, but vibrating between 1.414 with 1.415.

So here, we have PHYSICS making a PROOF OF MATHEMATICS that says, whether AP is correct or Old Math is correct.

AP

[Archimedes Plutonium]

Alright, on Amazon I see a few books on Finite Math

Margaret Lial in 10th edition

then there is

Larry Goldstein in 11th edition

then there is

Margaret Lial with Finite Math and Calculus in one book

then there is

Howard Rolf

then there is

Daniel Maki

then there is

Michael Sullivan

then there is

Stefan Waner

then there is

Jeffrey Watt

then there is

Goldstein, Schneider, Siegel

then there is

Frank Wilson

What I want is the book that was written to teach, not a book written in which the author is a poor teacher. I do not want another Apostol like book, nor do I want another Feynman type lecture book. These books are written for those who already know the subject well and not designed for teaching.

So, I want the Stewart type book for Finite Math.

AP

[Chris M. Thomasson]

On 6/30/2017 11:26 PM, Archimedes Plutonium wrote:
> On Friday, June 30, 2017 at 1:53:22 PM UTC-5, Chris M. Thomasson wrote:
>
>>
>> Fwiw, for instance, if somebody said they need two integers to represent
>> 4 digits of pi, including the leading 3, to fit their personal needs, well:
>>
>> 512 / 163 does the trick.
>>
>> That's all they need, and these integers do the trick.
>
> And that is the whole point of the idea-- every irrational number is two rationals that compose the irrational number.

[...]

Using your new math system, how can I use it to find two integers a and
b where a / b gives me 16 digits of pi including the leading 3 before
the decimal point? I can do it with convergent of continued fractions,
but you seem to think that's old math.

Please teach me how to find these two integers using your system.

[Julio Di Egidio]

On Friday, June 30, 2017 at 8:31:32 PM UTC+2, Archimedes Plutonium wrote:
> On Friday, June 30, 2017 at 12:58:19 PM UTC-5, Julio Di Egidio wrote:

<snip>

> > No, he is totally correct: that in fact exists (*) as mathematics of the
> > finite and it does have guaranteed correctness, based on the so called
> > containment constraint, i.e. that all solutions are guaranteed to be
> > bounded by the returned interval, and the quality of an implementation
> > is in the sharpness of the interval: it's standard mathematics that
> > really is broken...
> >
> > (*) The reference book is this one:
> > <https://books.google.it/books?id=tY2wAkb-zLcC&lpg=PR3&ots=IiGVRs0ipP&dq=global%20optimization%20using%20interval%20analysis&lr&pg=PR3#v=onepage&q=global%20optimization%20using%20interval%20analysis> Note that, despite the title, the book contains the full development,
> > from arithmetic to analysis.
>

> Thanks Julio, two questions please. Is there a real nice textbook on
> Finite Mathematics, one comparable as what the Stewart Calculus book
> is to calculus-- written by someone interested in teaching calculus.

Sorry, I don't know. The book I have linked to does provide the full
formal development, but in a condensed form, I'd say more suited to the
mathematician or the practitioner (lots of algorithms are presented, not
just the formal development of definitions and operations, but nothing in
terms of presenting or deriving the usual calculus, if not to specify
relevant differences or departures).

> Second question, please, am I the only mathematician that is adamant of
> getting rid of all negative numbers and Graphing in 1st Quadrant Only. Is
> there another mathematician on that same program?

Not any mathematician that I know of, but I really know very little about
the literature. The only guy I know of that is pursuing that route is Tim
Golden with his polysigned numbers (*): making a long story short, he is
trying to use positive numbers only and simplicial coordinates.
(*) <http://www.bandtech.com/PolySigned/>

To be honest, I do not see the point in getting rid of negative numbers:
why should the ray be more fundamental than the line? Indeed, FWIW, I
lean towards the line being more fundamental, for one thing because in
the construction of any numeric system I find myself needing (signed!)
integers to begin with...

Julio

[Julio Di Egidio]

On Friday, June 30, 2017 at 8:53:22 PM UTC+2, Chris M. Thomasson wrote:
> On 6/30/2017 11:44 AM, Chris M. Thomasson wrote:
> > On 6/30/2017 11:39 AM, Chris M. Thomasson wrote:
> >> On 6/30/2017 10:58 AM, Julio Di Egidio wrote:

<snip>

> >>> No, he is totally correct: that in fact exists (*) as mathematics of the
> >>> finite and it does have guaranteed correctness, based on the so called
> >>> containment constraint, i.e. that all solutions are guaranteed to be
> >>> bounded by the returned interval, and the quality of an implementation
> >>> is in the sharpness of the interval: it's standard mathematics that
> >>> really is broken...
> >>>
> >>> (*) The reference book is this one:
> >>> <https://books.google.it/books?id=tY2wAkb-zLcC&lpg=PR3&ots=IiGVRs0ipP&dq=global%20optimization%20using%20interval%20analysis&lr&pg=PR3#v=onepage&q=global%20optimization%20using%20interval%20analysis>
> >>> Note that, despite the title, the book contains the full development,
> >>> from arithmetic to analysis.
> >>
> >> Thank you for that.
> >
> > Wrt my comment about using two integers to represent a given precision
> > of an irrational, well, its correct up to that given precision.

But a stricter way to say that is that it is (almost) never correct.

> > We cannot gain two finite integers to represent an infinite irrational.

That's right, but we were talking of two rationals, not two integers:
the intervals I was mentioning are sets of rationals, in particular with
rational endpoints, plus they are all closed intervals.

> Fwiw, for instance, if somebody said they need two integers to represent
> 4 digits of pi, including the leading 3, to fit their personal needs, well:
>
> 512 / 163 does the trick.
>
> That's all they need, and these integers do the trick.

What the set-containment approach would give you is an interval like
[3.141; 3.142], or [3.1415; 3.146], etc. which in any case is guaranteed
to contain the solution. But you'll really have to study the system I was
referring to, I cannot do it justice but I must stress that it's much more
than just about error bounds. OTOH, at least I hope you can now see how an
irrational numbers ends up being the empty space between two rationals: in
a finitary, which also means effective, setting...

Julio

[j4n bur53]

This remindes me of W. Mückenheim, when he tried to refute
that there is a bijection between N and Q, i.e. a function
f : N -> Q, which is bijection.

I told him, look W. Mückenheim, if you get a chain of intervals,
than this is nothing else than a real number. So basically
he wanted to show that there is no bijection to

the rational numbers, but basically he showed Cantors result,
namely that there is no bijection to the reals. Its alas very
very simple:

Q : rational numbers

R : real numbers, can be mathematically construced from
N->Q, i.e. series a1,a2,... where a1,a2,.. etc..
are in Q, or can be mathematically construced from
N->QxQ, i.e. series i1,i2,... where i1,i2,.. etc..
are intervals i.e. pairs QxQ, or can be mathematically
constructed from subsets of Q, i.e. P(Q), dedekind cuts
etc.. etc..

Intervals is just another view on real numbers. Its not really
something different. A chain of internals is only then not
a real number, if you would have a fixed upper bound on the length.

But I am not sure whether you Julio believe that the upper
bound is 10^604 or some such. Otherwise if the chains are
not bound, its the reals. And if the chains are bounded

then for example with [3.141; 3.142], or [3.1415; 3.146], etc.
you cannot really compute as with pi. If you stop somewhere
I could produce finite formulas, that can fit on a usnet

post, that show its not pi.

Julio Di Egidio schrieb:

[Chris M. Thomasson]

Agreed.

> But you'll really have to study the system I was
> referring to, I cannot do it justice but I must stress that it's much more
> than just about error bounds. OTOH, at least I hope you can now see how an
> irrational numbers ends up being the empty space between two rationals: in
> a finitary, which also means effective, setting...

Yes. Of course an irrational is between two rationals. I hope I did not
come across as trying to deny that fact. Sorry if I did.

[Julio Di Egidio]

You keep missing the point, which is ideal point-like numbers that we
can never reach vs. effective and guaranteed enclosures. Just study
the thing before assuming it's the usual soup, it isn't. -- BTW,
even the function graphers benefit from those number: not even anymore
the problem of drawing lines that go up vertically, anyway better graphs
overall: because, again, these numbers (in the general case) are
intervals, not points...

Julio

[Chris M. Thomasson]

Not exactly sure how I missed the point, need to study it more. For
instance, pi is guaranteed to be in the interval between:

[3.1415926535;3.1415926536]

This is a given to me. Of course pi is in there, and gives more precise
graphs wrt resolution of the plane. AP talks about 100 grid and 1000
grid, well, the higher the resolution the more precision we can gain, of
course. Think of plotting a fractal in a 64x64 bitmap, vs plotting one
on a 2^32 by 2^32 bitmap. The more AP increases the plotting resolution,
the more precise plotting an irrational number will become.

[Archimedes Plutonium]

On Saturday, July 1, 2017 at 5:01:01 PM UTC-5, Chris M. Thomasson wrote:

>
> Not exactly sure how I missed the point, need to study it more. For
> instance, pi is guaranteed to be in the interval between:
>
> [3.1415926535;3.1415926536]
>
> This is a given to me. Of course pi is in there, and gives more precise
> graphs wrt resolution of the plane. AP talks about 100 grid and 1000
> grid, well, the higher the resolution the more precision we can gain, of
> course. Think of plotting a fractal in a 64x64 bitmap, vs plotting one
> on a 2^32 by 2^32 bitmap. The more AP increases the plotting resolution,
> the more precise plotting an irrational number will become.

Chris, in Grid Systems we can go from 10 Grid up to 10^604 Grid, but all of ordinary day to day math is carried out in 100 to 1000 Grid. A math textbook rarely goes beyond 10^4 Grid.

The only thing that really changes is that no curves exist, no continuum exists and infinity has a borderline. What is there not to like about all this cutting away of fiction in math.

As I asked BKK in another thread, why do mathematicians never want to clean up their house and get it in order, are they lazy and sloppy. Have they never been asked to clean up messes and rather just let decay and filth build up all around them. Or is it the fact that in math, unlike the other sciences, where no Judge of true math is the Nature Experiments of Nature, whereas in math, what is deemed true is all mind bending concoctions of ivory towered nitwits of math. In early 1990s we had Pons and Fleischman in physics screaming fusion in a test tube by palladium with electricity run through. By 1995, physics experiments disproved the physics nitwits. But in early 1990s we had the Wiles nitwit with his kookery of a proof of Fermat's Last Theorem, and because math is based on some kook-judges, not Mother Nature's unbiased science experimentation, thus, the Wiles idiocy of FLT was borne and now prospers as a horrible ugly blight and kook math.

Chris-- your own love of Fractals, is based in large part on kook math of Infinity as a foggy, opinion, shared by most professors of math who love foggy mess and trash, and never able to want to clean house. Funny, how a true science-- Quantum Electrodynamics wants to and needs to toss infinities out onto the trash pile in Renormalization, while the math cousins to physics, want to embellish their idiotic infinity with fractal designs.

Somehow, Chris, you escaped studying LOGIC more than studying math kookery of infinity and fractals.

AP

[Chris M. Thomasson]

We can actually store real data in fractals in the roots of complex
numbers. Why must you call me a kook? Afaict, your grid system is
exactly the same as increasing the size of the plotting plane to gain
more details. Fractals have an infinity border as well: Inside vs
Outside vs escape time algorithms.

Imho, you are pretty mean wrt calling other names like kook. Wow. Well,
at least I thank you for giving negative numbers a chance in your new
math. Negative charges are one aspect?

Fractals are real in the sense that we can build real, useful things
with them. Antennas?

http://www.fractenna.com

Btw, how do I use your system to gain two integers that can give me a
ratio up to a given precision wrt a number of digits for an irrational?

[burs...@gmail.com]

Even my bank account balance goes over 10^4 cents (He He).
Do you wear your fruit hat just now AP, doing the chicken dance?

P.S.: Do you mean a square grid, so 10^8 cents? Well, well,
you know those Swiss, its all chocolate and gold.

[j4n bur53]

Some facts:
Credit Suisse Group AG has bilanz sum (activa):
819’861'000'000 CHF
This is already more than 10^8 CHF.

Oracle Database has a Datatype Number, which
is up to 38 significant digits
https://docs.oracle.com/cd/B19306_01/olap.102/b14346/dml_datatypes002.htm

Java has a Datatype BigInteger, which
has so many digits, as your RAM gives you.
https://docs.oracle.com/javase/7/docs/api/java/math/BigInteger.html

With BigInteger you can easily compute with 10^604, your
infinity border. Here is an example calculation with your
infinity border:

?- X is 10^604, Y is root3(X).
X = 100000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000,
Y = 2154434690031883721759293566519350495259344942192108582
48923550634641110664834080018544150354324327610126122049178
09204465575051000832749571206753778093319327305836534892638
28125496931403878382796863315.

You can check yourself that Y is the 3rd root of your
infinity border, using an "interval" check:

?- ..., Z is Y^3, T is ((Y+1)^3).
Z = 9999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999
99999999999999999999999999997750102057162104088284680564669
06329302372725882236394411979142601586701096697325833038272
11015371495483174064309997945010904640277371399121069907211
47775295134486859541186906338398539485853664362726534562483
04768438514647915310208981117198217449183036698318772690132
35578427212210126762391487674849776130821581310109855310977
81940037654148392074565107575381404536559637168506668128772
421602229929780875,
T = 1000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000
00000000000000000000000000000000000000000000000000000000000
00000000000000000000000000001167486855800044076551490961742
74030226777746338560948570718700020702006200455077369002599
33794251289072947331115796008962621274890224463044193957906
23841924795980966113071439520196292217875467250585002751912
69630965037754215005111365672656779271257954707540900288566
50400393928486225675250373749741520424378159614657348024167
91158910677412658485766019034535433985111016182941007036612
8562348786698738496

So all this hogwash about intervals works also if you
fix the width of an interval to lets say eps = 1/10^n.
You then need only one number to represent it.

For example if you have a grid 1000, you don't need two
numbers to represent the interval [1.414,1.415], you
could also say 1.4145 for example the middle of it.

So middle numbers would be intervals:

1.4145 = [1.414,1.415]

And non-middle numbers, would be just points:

1.414 = 1.414
1.415 = 1.415

So you only need an additional one bit. This was pursued
I guess in unums, https://en.wikipedia.org/wiki/Unum_%28number_format%29
not 100%, its a little bit obscure what unums are, there
are different versions of it.

But lets assume we work with middle numbers only and
a fixed interval width, then most of the algorithms
boil down to some bisection. I used bisection for root3 above,
here is the code if isqrt,

square root. But the square root of 10^604 isn't very
interesting. Its just 10^302. But anyway, here have the
code of isqrt:

/**
* isqrt(X, Y):
* The predicate succeeds in Y with the integer square root of X.
*/
:- public isqrt/2.
isqrt(X, _) :- X < 0,
throw(error(evaluation_error(undefined),_)).
isqrt(0, R) :- !,
R = 0.
isqrt(X, Y) :-
Lo is 1<<((bitlength(X)-1)//2),
Hi is Lo*2,
sys_bisect(Lo, Hi, X, Y).

% sys_bisect(+Integer, +Integer, +Integer, -Integer)
:- private sys_bisect/4.
sys_bisect(Lo, Hi, X, Y) :-
Lo+1 < Hi, !,
M is (Lo+Hi)//2,
S is M*M,
sys_bisect(S, Lo, Hi, M, X, Y).
sys_bisect(Lo, _, _, Lo).

% sys_bisect(+Integer, +Integer, +Integer, +Integer, +Integer, -Integer)
:- private sys_bisect/6.
sys_bisect(S, Lo, _, M, X, Y) :- S > X, !,
sys_bisect(Lo, M, X, Y).
sys_bisect(S, _, Hi, M, X, Y) :- S < X, !,
sys_bisect(M, Hi, X, Y).
sys_bisect(_, _, _, Y, _, Y).

So basically you need an upper bound and a lower bound to do
your search efficiently. But if the curve you are searching is
not montone, you need to do other stuff. But a bound is
always helpful I guess.

You might find this bound interesting:

It is possible to determine the bounds of the roots of a polynomial
using Samuelson's inequality. This method is due to a paper by Laguerre.
https://en.wikipedia.org/wiki/Properties_of_polynomial_roots#Polynomials_with_real_roots

burs...@gmail.com schrieb:

[Archimedes Plutonium]

Hi Julio,

Well, not getting rid of them, just ignoring them, as ignoring even all the positive irrationals. If I have to ignore positive irrationals, knowing they exist as the empty space between Rationals, I have to be logical in ignoring all negative numbers for they are irrationals. Getting by in mathematics with just the Positive Rationals. If I have to ignore the positive rationals because math is precision, and how can one be precise in choosing between two pairs of numbers for square root of 2, then it would be bad to not ignore negative numbers.

I admit they are there, they exist, but I have to ignore them as not giving precision to math. Every time a irrational or a negative number is used in physics, they lose precision of mathematics in their usage.

The two places that are the most difficult to ignore the negatives is negative charge in physics and negative slope in Y = mx + b.

In common everyday life, the negative finance accounting is not really negative numbers but is rather-- subtraction. No-one in banks are multiplying a negative dollars by negative dollars and coming up with positive hard cash dollars. No-one in physics knows of a negative gold atoms, nor a negative angle of 30 degrees, nor a negative area of a integral of sine or cosine. Negative objects simply do not exist and it is failed and weak minds of people that turn a imagination into fakery. Same goes for believing ghosts and witches are as real as people. Sorry, I am lecturing here for the benefit of Chris, only it will glide over his head.

It never dawned on me that a line has a positive and negative side, while a ray has just one. But I would think the ray is more fundamental than the line, because let us say the Universe is Euclidean, and you start out somewhere, anywhere in the plane, we can consider your start point as a "wall" a start wall and so, the line is a ray. Now if the Universe is not Euclidean open but the surface of a sphere, you start somewhere and you go around and come back to your starting point, that too is a ray. So, no matter if the physical universe is a Euclidean space or a Elliptic geometry space, a ray is more fundamental than a line which has arrows on both ends.

I am not throwing negatives away, julio, I admit they are there, serving a useful function of being space, empty space, just as the positive irrationals in between rationals is empty space.

But what I want to do is always move functions from the 4 quadrants so that they all just reside in the 1st Quadrant Only. So the equation of a ellipse, centered at (0,0) has to be moved so all its parts are in 1st Quadrant Only. The sine and cosine functions have to be lifted so they oscillate in 1st Quadrant Only.

So I think the teaching of Graphs and functions in the future of mathematics should be done all in 1st Quadrant Only, and never ever teach the 4 quadrants until in some graduate course in college. Leave out the notorious other 3 quadrants.

Now, sometimes negatives are used for direction sake, so that a negative slope m in Y = mx+b, is merely there to warn us the line is slanted downwards from left to right. So the negative sign itself is a direction indicator but does that warrant the other 3 quadrants? I think not. In integrals, negative area indicates area below the x-axis. In physics the negative charge versus positive charge, is hard to say what the negative sign is doing to the quantity of 1 unit of charge, is it again a directional aspect. So the signage plays some different role from the quantity of a number. And since we really do not know what signage means other than positive signage, it is best to never treat the other 3 quadrants the same weight of importance as the 1st Quadrant Only.

AP

[j4n bur53]

Bisection is fast. Here is some timing:

?- X is 10^604, time(_ is root3(X)).
% Up 4 ms, GC 0 ms, Thread Cpu 0 ms (Current 07/02/17 01:59:32)

Ok lets do it 1000-times:

?- X is 10^604, time((between(1,1000,_), _ is root3(X), fail; true)).
% Up 1,355 ms, GC 3 ms, Thread Cpu 1,343 ms (Current 07/02/17 02:00:50)

The above 1,355 is 1355. So divide by thousand, it takes
around 1.4 ms to take the root3 of the AP infinity border
on a modern PC.

j4n bur53 schrieb:

[j4n bur53]

Changing topic to even more nonsense? Your fruit
hat on your head, and dancing like a Dervish?

Archimedes Plutonium schrieb:

[burs...@gmail.com]

Yes, wiki writes:
"a u-bit, which determines whether the unum corresponds
to an exact number (u=0), or an interval between
consecutive exact unums (u=1)"

[Chris M. Thomasson]

[...]

AP, how do I create my vector field DLA field without using negative
numbers. Here is the online program:

http://funwithfractals.atspace.cc/ct_fdla_pa_t0

Can you run this on your computer? The DLA process is built from a
single attractor in the center. Each hit from the rays cast from the
circle creates new attractors, and ultimately builds a DLA cluster.

The code is in the site. Take a look at it. How would this look using
your new math?

Thanks.

[Chris M. Thomasson]

When I wrote this code, I did not even think about trying to remove
negative numbers. Fwiw, the code for the actual vector field is:

http://funwithfractals.atspace.cc/ct_fdla_pa_t0/ct_field.js

How do I remove negatives from this and still have it work? Btw, AP, DLA
is real:

https://en.wikipedia.org/wiki/Diffusion-limited_aggregation

They are fractals. Now, I want you to help me rewrite this using only
positive numbers in your grid system without bloating the code with a
bunch of contrived garbage. Can you help?

[Archimedes Plutonium]

On Saturday, July 1, 2017 at 8:20:09 PM UTC-5, Chris M. Thomasson wrote:
(snipped)

Well it is good to see your parent's expense in your education was not for waste.

>
> When I wrote this code, I did not even think about trying to remove
> negative numbers. Fwiw, the code for the actual vector field is:
>

I did say that some negatives are unavoidable such as the Y = mx +b with negative slopes. Negative numbers embody direction.

>
> How do I remove negatives from this and still have it work? Btw, AP, DLA
> is real:
>
> https://en.wikipedia.org/wiki/Diffusion-limited_aggregation
>
> They are fractals. Now, I want you to help me rewrite this using only
> positive numbers in your grid system without bloating the code with a
> bunch of contrived garbage. Can you help?

Well, no, for until you define a fractal, none exist. Now, watch, watch Chris closely and carefully as he tries to define fractal, for he will not start out defining what infinity is, not at all, but use infinity throughout. Why you did not take Logic in school Chris, instead of all that drama and dance class.

You have never defined a fractal. And in another thread I am discussing the definition of Curve in Old Math. A total disgusting pile of garbage of a definition. Your fractal notion is probably a better piece of crap nonsense than was Old Math's Curve.

But, I do not have time for your fractal phony baloney, for just focusing on one piece of math crap is enough of a challenge.

AP

[Julio Di Egidio]

I said an interval, not a point in an interval: in a (*proper*, as in correct and not an imperial fraud that goes on for centuries) mathematics
of the finite, an irrational number just *cannot be a point*. And yes,
you'd have to study it, or just believe me...

That said, even if you cannot care less for what's correct and what's a
gigantic fraud, that math is still *way* better for practical purposes!

HTH,

Julio

[Julio Di Egidio]

On Sunday, July 2, 2017 at 1:59:10 AM UTC+2, Archimedes Plutonium wrote:
> On Saturday, July 1, 2017 at 8:20:33 AM UTC-5, Julio Di Egidio wrote:

<snip>

> > To be honest, I do not see the point in getting rid of negative numbers:
> > why should the ray be more fundamental than the line? Indeed, FWIW, I
> > lean towards the line being more fundamental, for one thing because in
> > the construction of any numeric system I find myself needing (signed!)
> > integers to begin with...
> >

<snip>

> It never dawned on me that a line has a positive and negative side, while
> a ray has just one. But I would think the ray is more fundamental than the
> line, because let us say the Universe is Euclidean, and you start out
> somewhere, anywhere in the plane, we can consider your start point as a
> "wall" a start wall and so, the line is a ray.
>
> Now if the Universe is not Euclidean open but the surface of a sphere, you
> start somewhere and you go around and come back to your starting point,
> that too is a ray. So, no matter if the physical universe is a Euclidean
> space or a Elliptic geometry space, a ray is more fundamental than a line
> which has arrows on both ends.

Yes, that makes sense, too. Or, one could even just notice that the
the most common construction of the integers simply adds a sign to the
naturals. Which is all very sensible, it even corresponds to the actual
development of numbers we attribute, via anthropology, to our cultures.

OTOH, mathematics really is a strange beast and I have a hunch that we
might really be talking logic there, not mathematics: mathematics must
implement ideas that are logical, but mathematics per se is formal, and
really I have tried and tried and I have found no way to define any
natural numbers in any formal language unless I have a pre-formal,
"infrastructural" signed integers I can use for the construction of the
very language I am using to define the mathematics!

It's still an open investigation for me, but here is an example of the
distinction I have in mind: back to the history of the development of
numbers, it's true that negative numbers came much later than the simple
counting, in fact they even had to wait for zero to be conceived, OTOH,
if you think about it, zero really did exist since time immemorial, as
an absence, and negative really did exist since time immemorial, as the
lack of something (below vs. above), what did take very long is for
those notions, which were already logical, to appear and be defined in
mathematics!

But I am stil thinking about it... Thanks for sharing your thoughts.

Julio

[Archimedes Plutonium]

Hi Julio, how much physics have you studied, and are you open to the idea that physics is the king and math is the minor subset inside of physics. Are you open to that idea?

I really believe that no-one can master math without the idea that one must look to physics for the answer to any big problem arising in math.

> It's still an open investigation for me, but here is an example of the
> distinction I have in mind: back to the history of the development of
> numbers, it's true that negative numbers came much later than the simple
> counting, in fact they even had to wait for zero to be conceived, OTOH,
> if you think about it, zero really did exist since time immemorial, as
> an absence, and negative really did exist since time immemorial, as the
> lack of something (below vs. above), what did take very long is for
> those notions, which were already logical, to appear and be defined in
> mathematics!
>

So with the idea that physics is number 1 and math a subset of physics we all know numbers-- existed with the periodic table of chemical elements long before minds conceived of 1, 2, 3, ...

Of course, humans counted their fingers and toes long before they counted in chemistry. But this signifies math is more than just an abstraction, but that math has concrete physical reality. This must be so since math is subset to physics.

Before the Atom Totality theory, everyone in math with problems sought refuge in "philosophy" a huge mistake. Now in Old Math they would say the number 3 is not going to show up at your front door. But not true for if a mineral of lithium showed up then both lithium and 3 showed up.

If someone drew a triangle, knocked on your door, you open it, and the triangle is displayed, you have physically a triangle and the number 3, for legs , 2 and 3. Now you also have there -3. In that starting with vertex going counterclockwise is +3 in circumnavigating the triangle, but going clockwise around is -3.

> But I am stil thinking about it... Thanks for sharing your thoughts.
>
> Julio

How much physics have you had and do you like it?

Especially the Maxwell Equations, are you comfortable with them?

AP

[Julio Di Egidio]

I'd pretty much subscribe 100% to what you have said above, including the
fact that mathematics really has no direct link to philosophy, except that
wherever you say physics I'd say logic. And now this divergence between
us, about what "governs" mathematics, I think ends up being a genuine
philosophical problem, namely the problem of what the ultimate nature of
reality is. But we could ignore the philosophical problem and then we are
saying exactly the same thing...

> > But I am stil thinking about it... Thanks for sharing your thoughts.
>

> How much physics have you had and do you like it?
>
> Especially the Maxwell Equations, are you comfortable with them?

I love physics, Einstein was my hero as a kid. But, besides my engineering
level studies, I have tried to study some more lately, net a couple of years
by now, but really focused to understanding the presently open problems.
My main interests are in cosmology on a side, of course, and quantum
information theory specifically, but that's in particular because, as a
programmer, I'd like to get good at it... I wish I had had the time to
study Maxwell's classical theory of electromagnetism, they even say it's
beautiful, but not so far: in the meantime I am simply trusting Einstein! :)

Julio

[burs...@gmail.com]

Asking for physics being king over math only shows how
stupid you are AP. Math as a modelling language for
physics models makes much more sense. For example we
can derive results, which are somehow independent of

the actual physics. Take this theorem:

"Gauss's Theorema Egregium (Latin for "Remarkable
Theorem") is a foundational result in differential
geometry proved by Carl Friedrich Gauss that
concerns the curvature of surfaces. The theorem
says that the Gaussian curvature of a surface
does not change if one bends the surface
without stretching it."
https://en.wikipedia.org/wiki/Theorema_Egregium

We might not know exactly how the surface around us
is formed, nevertheless the above theorem applies
always, provided the assumptions in the theorem
are satisfied. So drawing a line between math and

physics helps in obtaining more general mathematical
results, that can then be applied to actual physical
models independently. But is this too bizar for you
AP? You rather prefer continuing making a mess?

[Markus Klyver]

Den onsdag 28 juni 2017 kl. 20:42:56 UTC+2 skrev Archimedes Plutonium:
> Newsgroups: sci.math
> Date: Wed, 28 Jun 2017 11:31:39 -0700 (PDT)
>
> Subject: place this proof in the Math Array//Proof that No Curves exist and No
> Continuum exists
> From: Archimedes Plutonium <plutonium....@gmail.com>
> Injection-Date: Wed, 28 Jun 2017 18:31:40 +0000
>
>
> place this proof in the Math Array//Proof that No Curves exist and No Continuum exists
>
> On Wednesday, June 28, 2017 at 12:33:22 AM UTC-5, alouatta....@gmail.com wrote:
> (snipped)
> >
> > See what you can do with the fourth power.
>
> Actually, it appears as though the higher the power, the more accurate the derivative and integral converges to the power rule without even having to go to higher Grids of 100 or 1000. For example at 5x^4, the integral and derivative come close to the Power Rule.
>
> But, now, what I need to do especially is show that the GEOMETRY of the hinge at the midpoint produces all of calculus, and this can occur only if the derivative is itself part of the function graph as a straightline segment.
>
> You cannot have a Calculus where the integral rectangle is a box with a curved top to the box, or, where the derivative is a curve segment.
>
> The ability of the hinge box to be the Proof of the Fundamental Theorem of Calculus FTC, a geometry proof is ample warning enough, that Old Math Calculus with their Limit involved proof, is old decayed and invalid.
>
> The below diagrams of a Calculus Chain, is ample proof that NO CURVE and NO CONTINUUM can exist in math, for it destroys the Calculus.
>
> Calculus can only exist is Space as a coordinate system is DISCRETE with gaps and holes in between points of a function and points of the graph. Discrete Math rules all of mathematics. Shame I never took Discrete Math in school, even though I had ample opportunity. I should have taken it, instead I remember taking Differential Geometry, and learned little. My rebelliousness was apparent to me, even at the young age of 20, but it was rebelliousness, not learned, but rather, was already inside my mind that I had a steadfast notion of what math was good and what needed repair. Of course, at such a young age striving for grades, I was not about to rebell in class or to the teacher, for then, you had to conform. But a course in Discrete Math would have been good for I would have had at least some raw overview of Discrete Math.
>
>
> diagrams of the chain x^5, 5x^4, 20x^3, 60x^2, 120x Re: no Curve, no Continuum exists in math, proving by a Calculus Chain
>
> Preparing for tomorrow, and need to check for mistakes.
>
> Tomorrow is here and found no mistakes, but now need to make abundantly clear.
>
> This chain of derivatives (descending) and integrals (ascending) is a proof that no curves exist and no continuum exists. It means all of math is discrete with holes and gaps between Rationals. It means that no curve, even the circle is but tiny fine straightline regular polygons.
>
> Now I need to check the below for errors, but what it shows is that the Calculus is all based upon a rectangle for integral area and a hinged right triangle, its hypotenuse for the derivative. It means the derivative is part of the starting function graph itself, and that a derivative of a tangent to a curve is poppycock nonsense.
>
> function 120x
>        132
>         /|
>       /  |
> 120/----|
>   /      |
> /        |
> |        |
> |        |
> |        |
> _____
> .9  1  1.1
>
>
> derivative of 120x as equal to 120 where dy/dx at x=.5 is 60/.5 = 120, and x=1 dy/dx = 120/1 = 120
>        120
>         /|
>       /  |
>  60/----|
>   /      |
> /        |
> _____
> 0  .5  1
>
>
> integral of 120x as box 1 * 60 as 60x^2 is 60 when x=1
>
> ______ 60
> |         |
> |         |
> |         |
> ----------
> 0       1
>
>
> xxxx
> Alright, good, that first one was itself a straightline of Y = mx + b and all straightlines in calculus are going to be easy on derivative and integral. But notice, where few have ever noticed, that the integral of a Y = mx + b, pushes the starting function into being a curve of 2nd degree polynomial or function. So, here is the problem of Old Math-- do they ignore the fact that integral is a curve while the function itself is straightline and derivative is straightline. Ever since Leibniz and Newton, everyone just ignored this fact of mixing up straightlines and curves in Old Math. But I do not ignore it, and state further, that all of Calculus is just straightline segments. That the integral of 120x as 60x^2 is itself a bunch of tiny straightline segments 60(x)(x) where (x) is a straightline.
> xxxx
>
>
>
> function 60x^2
>         72.6
>         /|
>       /  |
>  60/----|
>   /      |
> /        |
> |        |
> |        |
> |        |
> _____
> .9  1  1.1
>
>
> derivative of 60x^2 as equal to 120x is dy/dx for x=.5 is 60/.5 = 120, and x=1 is 120/1 = 120
>
>        120
>         /|
>       /  |
>  60/----|
>   /      |
> /        |
> _____
> 0  .5  1
>
>
> integral of 60x^2 is 20x^3 as box .2 * 60 = 12 as 20x^3 interval .9 to 1.1 is 26.62 - 14.58 = about 12
>
> ______ 60
> |         |
> |         |
> |         |
> ----------
> .9       1.1
>
>
> xxxx Now notice how cool the hinged box integral works, where you lift the box at midpoint, forming a trapezoid, and remember the trapezoid rule in Calculus? So the hinged box does not come from-- out of nowhere-- but is already a integral part of calculus. And all the more reason, that Calculus is all about tiny straightline segments. You cannot make the integral and derivative as INVERSES of one another, if you have to shift between being a "curve and being a straightline segment". The only way you can have derivative inverse integral, is if you work in only one medium-- all straightline segments.
> xxxx
>
>
> function 20x^3
>        26.62
>         /|
>       /  |
>  20/----|
>   /      |
> /        |
> |        |
> |        |
> |        |
> _____
> .9  1  1.1     where x=.9, y= 14.58
>
>
> derivative of 20x^3 as equal to 60x^2, but from function graph is dy/dx 6.62/.1 is approx 60 made better in 1000 Grid
>
>        60
>         /|
>       /  |
>   5 /----|
>   /      |
> /        |
> _____
> 0  .5  1
>
>
> integral of 20x^3 as box .2 * 20 = 4 as 5x^4 interval .9 to 1.1 as 7.32 - 3.28 = 4
>
> ______ 20
> |         |
> |         |
> |         |
> ----------
> .9       1.1
>
>
> xxxx So, here in this CHAIN of Calculus of either ascending integrals or descending derivatives, we see that the Box calculus with its hinged midpoint solves every calculus problem. But in solving, it can only work if the derivative and integrals are all straightline segments, connecting Discrete points of a graph system, where there are holes and gaps in between. In Old Math, what they did, is play around with Limits, for they knew they had a problem of ever proving INVERSE in the FTC. They never had a notion that curves do not and cannot exist, so they came up with the goofy idea of playing around with Limits. To me, what the limit is like, is like hiring a seance telepathy person to make contact with the dead deceased and long buried people. The Limit voodoo dance.
> xxxx
>
>
> function 5x^4
>
>
>        5
>         /|
>       /  |
> .31 /----|
>   /      |
> /        |
> _____
> 0  .5  1
>
>
>
> derivative of 5x^4 as equal to 20x^3, but from function graph is dy/dx is 7.32-3.28 = 4 for dy and .2 for dx is 4/.2 is approx 20, and from formula is 20*1 = 20
>  
>        7.32
>         /|
>       /  |
>   5/----|
>   /      |
> /        |
> |        |
> |        |
> _____
> .9  1  1.1     where x=.9, y= 3.28
>
>
>
> integral of 5x^4 as box .2 * 5 = 1 as x^5 interval .9 to 1.1 as 1.61 - .59 = 1
>
> ______ 5
> |         |
> |         |
> |         |
> ----------
> .9       1.1
>
> Alright, good, that CHAIN worked out fine. It is the content of a proof. A proof that mathematics has no Curve and has no Continuum. For if it had either one or both of those, then Math cannot have Calculus.
>
> It is a picture proof of the Theorem Statement:: Math has no curve and no continuum, because math has a Calculus with a Fundamental Theorem of Calculus.
>
> Proof Statement:: the above pictures is a proof. QED
>
> AP

"Calculus can only exist is Space as a coordinate system is DISCRETE with gaps and holes in between points of a function and points of the graph."

Are you always this stupid?

[Markus Klyver]

Den torsdag 29 juni 2017 kl. 00:36:06 UTC+2 skrev Archimedes Plutonium:
> Alright, I am satisfied that those pictures are a proof of no curves/ no continuum exists in math, otherwise we lose Calculus. That is a loss too large. Now I need to trim that proof, because the statement is far smaller than the proof. If I can do just one picture, then I have the proper proof for Conservation Principle of Math. So I define the CHAIN of integrals and refer to the chain in the proof.
>
> Now a comment I made a few days ago is that the best proof of Math is a geometry argument. Now I wonder if that observation comes from human evolution that we evolved from apes throwing rocks and stones and where a brain evolves to "better throw" thus a evolution of a brain good with geometry in order to throw better. So, is the observation that a geometry proof is far better than a algebra proof, is that observation inside of math or is it due to our brains handling geometry better than handling algebra.
>
> I am asking if math itself has a proof that geometry proofs are better than algebra proofs?
>
> Aside from the fact that algebra is mostly abstract symbols whereas geometry is more about some substance of math, like drawing trapezoids and midpoints and right triangles in the No Curves Exist proof.
>
> Quite frankly, I would say no, that algebra proofs and geometry proofs are equal in -- proving ability or capability. But then again, when we look at how much is unproven in algebra compared to geometry we see the mountain pile at algebra and not so much unproved conjectures on the geometry side.
>
> The Atom Totality theory for which mathematics is but a tiny subset, would say that algebra and geometry are equals, no favoritism, and that our ease with geometry is a remnant of our evolution history.
>
> But, however, if we look at the most mathematical part of physics-- EM theory, the AP-Maxwell Equations, do we get a sense that Geometry is larger than Algebra. The Old Physics Maxwell Equations, those 4 differential equations are mostly geometry, not algebra. So, in this sense, there maybe something to the idea that geometry proofs are the best proofs possible.
>
> Another viewpoint is the history of mathematics, in that the first Logical system-- Euclid's Elements, is, afterall geometry, and axioms of geometry. Now for Algebra, a comparable system would have to wait until 1800s with Peano axioms for the Naturals, and covering only Naturals, whereas the Irrationals are still a mess. Number theory and ideas appear in Euclid, but just a add-on appendage.
>
> CHAIN CALCULUS;; let me explore this some more. I feel more fruit is in this.
>
> The chain I used was starting at x^5 and descending derivatives 5x^4, 20x^3, 60x^2, 120x, finally just 120. It is also a ascending integral.
>
> In a certain sense, the CHAIN itself is a Calculus of a Calculus. A calculus upon calculus. It is as if the microscope put the microscope under the lenses. Or the telescope focusing upon its ownself.
>
> x^5
> 5x^4
> 20x^3
> 60x^2
> 120x
>
> Now if x = 1 we have the sequence for derivative as 1, 5, 20, 60, 120 as derivatives which, unexpectedly is increasing while the starting function is decreasing, and this is alarming.
>
> And for the integrals we naturally expect a increasing integral area starting with 120x but instead, here again we are alarmed that the area decreases with starting function 120, 60, 20, 5, 1
>
> So, what gives here? We would expect from our senses that starting with x^5 would have a larger derivative than 120x and that x^5 a larger integral area than 120x.
>
> So our intuition is really battered by this. And instead of x=1, let us try x=2 or x=10. Now, when we use x=10, do we begin to get some normal behavior in this, for 10^5 is far larger than 1200.
>
> Now, let me start a NEW CHAIN, instead of starting up at x^5, let me start a new Chain with just x, the identity function Y=x
>
> x
> 1/2x^2
> 1/6x^3
> 1/24x^4
> 1/120x^5
>
> That is a Chain of descending integral and ascending derivatives.
>
> Now plugging in x=1 we have this progression for integrals 1, 1/2, 1/6, 1/24, 1/120
>
> which, to my mind is bizarre for that should be the derivative getting smaller not the integral getting smaller
>
> And now for the derivative sequence starting at 1/120x^5 is 1/120, 1/24, 1/6, 1/2, 1
>
> which should be the integral not derivative sequence.
>
> So, is the Chain somehow flipping around the integral and derivative?
>
> And here again, if we put in x=2 or x=10 we reverse the situation to being more normal.
>
> And, we have to ask, at what number, is a sort of midpoint in the Chains, to being normal?
>
> Is it perhaps the number 2.71 for x or perhaps 3.14 for x so that the Chain acts normal again.
>
> let me throw in x=3 to see if it begins to act normal
>
> x^5 = 243
> 5x^4 = 405
> 20x^3 = 540
> 60x^2 = 540
> 120x = 360
>
> Nope, no normal there, but normal with x=10
>
> x^5 = 100000
> 5x^4 = 50000
> 20x^3 = 20000
> 60x^2 = 6000
> 120x = 1200
>
> Normal there, but what is the number that it starts normal?
>
> And what is the meaning of all of this?
>
> AP

"I am asking if math itself has a proof that geometry proofs are better than algebra proofs?

Aside from the fact that algebra is mostly abstract symbols whereas geometry is more about some substance of math, like drawing trapezoids and midpoints and right triangles in the No Curves Exist proof.

Quite frankly, I would say no, that algebra proofs and geometry proofs are equal in -- proving ability or capability. But then again, when we look at how much is unproven in algebra compared to geometry we see the mountain pile at algebra and not so much unproved conjectures on the geometry side."

That depends on the context, and how rigorous you want to be.

[Markus Klyver]

Are you saying people in banking and physics never multiply negative numbers?