MATHOPEDIA-- List of 80 fakes and mistakes of Old Math// Student teaches professor
by Archimedes Plutonium

Last revision was 28Apr2022. And this is AP's 160th book of Science.

Preface:
A Mathopedia is like a special type of encyclopedia on the subject of mathematics. It is about the assessment of the worth of mathematics and the subject material of mathematics. It is a overall examination and a evaluation of mathematics and its topics.

The ordering of Mathopedia is not a alphabetic ordering, nor does it have a index. The ordering is purely that of importance at beginning and importance at end.

The greatest use of Mathopedia is a guide to students of what not to waste your time on and what to focus most of your time. I know so many college classes in mathematics are just a total waste of time, waste of valuable time for the class is math fakery. I know because I have been there.

Now I am going to cite various reference sources of AP books if anyone wants more details and can be seen in the Appendix at the end of the book.

I suppose, going forward, mathematics should always have a mathopedia, where major parts of mathematics as a science are held under scrutiny and question as to correctness. In past history we have called these incidents as "doubters of the mainstream". Yet math, like physics, can have no permanent mainstream, since there is always question of correctness in physics, there then corresponds questions of correctness in mathematics (because math is a subset of physics). What I mean is that each future generation corrects some mistakes of past mathematics. If anyone is unsure of what I am saying here, both math and physics need constant correcting, of that which never belonged in science. This then converges with the logic-philosophy of Pragmatism (see AP's book of logic on Pragmatism).

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Table of Contents
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1) Introduction

2) List of 80 errors, mistakes and fakes of Old Math.

3) Appendix

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1) Introduction

Alright, well, mathematics is a closed subject. What I mean by that is due to the textbook series of Archimedes Plutonium TEACHING TRUE MATHEMATICS, that once you learn the polynomial transform and learn the two Power Rules of Calculus, you reached the peak, the pinnacle of all of mathematics, and anything further in math is just details of what you learn in that textbook series. Math is a completed science because it has this "peak of calculus", unlike the other 5 hard sciences of physics, chemistry, biology, geology, astronomy. Those other five will continue to find new ideas, new things, while math remains static and complete to its peak of calculus understanding. Mathematics is finished complete as far as a science goes because the peak of math is going nowhere. And even though Physics will find new science such as how the proton toruses inside of atoms are configured in geometry, the geometry and calculus used in that configuration, that new science does not change nor does it create or require a new math peak/summit to handle the new physics.

Now I do need to discuss the errors of Math in general and the errors of math in geometry in particular. I have the feeling that Geometry is the more important of the two-- algebra - geometry. This list appears in partial form in most of AP's Teaching True Mathematics textbook series by Archimedes Plutonium, meant to be a guide and orientation, and a organizing of what must be covered before graduating from College, and what math to steer clear of.

Errors mostly, but not always, for some are included because too much time spent on them.

The listings in Mathopedia of errors, mistakes and fakes is based on the idea that Calculus is the supreme achievement of all of mathematics for it is the essential math of doing Physics electricity and magnetism. And in order to have a proof of the Fundamental Theorem of Calculus, we must clean up and clean out all the mistakes, fakes and errors of Old Math, erstwhile, we have no Calculus. So calculus is the consistency maker for the rest of all of mathematics.

2) List of 80 errors, mistakes and fakes of Old Math.

1) Calculus requires a geometry proof of Fundamental Theorem of Calculus, a proof that derivative and integral are inverses of one another, just as addition and subtraction are inverses, or, multiplication and division are inverses. The only way to obtain a geometry proof is to clean up and clean out all the fakes, mistakes and errors of Old Math, such as their fake numbers-- the Reals. Their fake definition of function allowing anything be a function. Their fakery of a continuum when even physics by 1900 with Planck onwards in Quantum Mechanics proving the Universe is discrete Space not a continuum, yet by 1900 onwards those in mathematics following the idiotic continuum in the Continuum Hypothesis with even more avid interest, when they should have thrown the continuum on a trash-pile of shame.

2) The true numbers of mathematics are the Decimal Grid Numbers, because you have to need and apply one mechanism only to obtain the true numbers of mathematics-- Mathematical Induction. In Old Math they had just a tiny few intelligent mathematicians, Kronecker, who emerged from the gaggle crowd of kooks to notice that Naturals all come from one single mechanism-- Mathematical Induction. But Old Math never had a crowd of mathematicians with logical brains to say-- all our numbers need to come from the one mechanism of Mathematical Induction.

3) The true numbers of math have empty space between successor and predecessor numbers. For example the 10 Grid is 0, .1, .2, .3, . . . , 9.8, 9.9, 10..0. Where no numbers exist between .1 and .2, etc. Only discrete numbers allow us to give a proof of Fundamental Theorem of Calculus.

4) All functions of mathematics must be a polynomial, and if not a polynomial, convert the offering to a polynomial over a specific interval. Old Math is caught with their pants pulled down and exposed by not having all functions be polynomials for the silly dumb and stupid analysis of a straight line being Y=mx + b is open to interpretation that the slope "m" must not be 0. When Old Math never realized all functions of math must be polynomials, the question of y_2 - y_1 / x_2 - x_1 never rears its ugly head in New Math.

Where is that stupid thread in sci.math, poising as a puzzle problem when it had no functions only pretend functions?

A few days back, 11Aug2021 appeared a stupid puzzle problem here in sci.math. Of someone pretending he had 3, 4 even 5 or 6 functions and wanting to prove equality.

Then I stepped into the conversation saying he had no functions at all, until they are converted into polynomials over a specified interval, then you can do calculus on those true real functions.

So, the world wide math community has got to begin to learn, no function is a function, until, and unless they are polynomials. This is an axiom of math and is proven true by the geometry proof of Fundamental Theorem of Calculus. You cannot have a FTC, if you have functions that are not polynomials.

So there is a trade off-- does math want calculus or no calculus? If you want calculus, all your functions have to be polynomials. This has to do with the concept of discrete geometry, not a continuum, for polynomials are discrete.

5) Space is discrete and all lines in space are strings of attached straight lines.

6) No curves exist in Geometry, only finer and smaller straight line segments attached to one another.
We can still keep the name "curve" as long as we know it is a string of fine tiny straightline segments strung together in what looks like a smooth curve. If curves exist, then the Calculus in Fundamental Theorem of Calculus cannot be proven and thus Calculus does not exist. We all know that we have to have Calculus, and so we throw out onto the trash-pile the curve of Old Math. And this is reasonable because starting in 1900 in physics there arose the Quantum Mechanics of Space being discrete. And a discrete space has no continuum, has no curve of Old Math.

7) Space has gaps in between one point and the next point. These gaps are empty space from one point to the next point, for example in 10 Grid there is no number between .1 and .2, and in 100 Grid there exists no number between .01 and .02.

8) Limit analysis was an insane fakery in Old Math, concocted because Old Math needed the excuse of some proof, so they invented the monster con-artist trick that a limit analysis would divert the fact it is no proof at all, but a Non Sequitur argument. Limit analysis is juju totem witchcraft dance around a desire to prove the Fundamental Theorem of Calculus. Just as idiotic as dancing around a sick person of a virus is going to cure the person. Analyzing something is not the same as proving "that something".

9) Infinity has a borderline and there is a microinfinity compared to a macroinfinity. For example in 10 Grid, the microinfinity is 0.1 if we exclude 0 and so there is no number smaller than 0.1 and no number larger than 10 in 10 Grid, where 10 is macroinfinity.

10) In New Math, true math, we must define infinite as something that separates finite number from infinite number. This means a border must exist between what we call a finite number and what is a infinite number. It just so happens we have two kinds or types of infinity, the large infinity, macroinfinity and the small infinity which is the inverse of the large infinity. The inverse is we divide large infinity into 1. There is no logical escape from having a borderline between finite and infinite. And amazing that not until AP happened to traverse on this concept-- you need a border, that this concept was undiscovered-- the demand and need of a borderline. Fortunately the history of mathematics had already done work on geometry figures with infinite reach and yet have finite area. For to uncover where this borderline was, AP needed to only review Huygens tractrix geometry work. Where does the area of the tractrix equal the area of the associated circle for the first time as the tractrix moves down the x-axis ( the pocketwatch experiment)? And it is no surprise to me that when that equality comes true is a special moment in the digit string of pi-number, 3.14159...... For the first time the area of tractrix equals the area of associated circle is where pi digits have their very first three consecutive 0 digits in a row. So the Tractrix proves the infinity borderline is 1*10^604. And naturally, microinfinity would be 1*10^-604.

11) In the discovery of the infinity borderline by AP in 2009, using Huygens tractrix proof of 1692. Once I had proven the infinity borderline was 1*10^604, I wanted another different proof that this was the true borderline of infinity. I wanted a geometry proof to see if the algebra proof was correct. And so I devised a supporting geometry proof that 1*10^604 was the true infinity borderline by seeing whether the 5 regular polyhedron of there angles and faces divide evenly into these pi digits where pi has three zeroes in a row. This means dividing the number by 120 = 5! = 5x4x3x2x1. And whether that 120 divides evenly into the pi number.

3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000

And sure enough, 120 divides evenly into those 604 pi digits ending in ...132000

But even more astounding is that 120 divides evenly into pi digits at the algebraic closure of pi, 1*10^1208. The Algebraic closure is where you multiply any _two finite numbers together_ and the result cannot exceed the algebraic closure. This string of 1208 digits of pi are also divisible by 120, telling me that at infinity, you have all the regular polyhedra in existence. (Note, by 2021, AP finds a 6th regular polyhedra, here to for unknown).