MATHOPEDIA-- List of 75 fakes and mistakes of Old Math. AP's 174th book. Soon to be published as a Kindle book. Details of all of these are found in already published Kindle books, such as the geometry proof of Fundamental Theorem of Calculus.

Last revision was 21Sep2021.

I added the correction of the Natural Logarithm Ln(x) to base 2.71... for its definition using Y= 1/x of an integral over an interval from 1 to x in 1/t dt is very much flawed and incorrect. It was a serendipity discovery that when taking the Ln(1.00005) the true value is exactly 0.00005 and not 0..000049998... The true definition of Ln(x) has to be from a geometry that allows for the equiangular logarithmic spiral. A Ln(x) based upon 1/x does not give a equiangular log spiral. What does give a equiangular log spiral are the Decimal Grid Number System where you have equal spacing of discrete numbers. So for example in Old Math their Ln(1.02) was 0.0198... while in New Math where we have a corrected and true Ln(x) that Ln(1.02) = 0.02 exactly.

11th published book
World's First Geometry Proof of Fundamental Theorem of Calculus// Math proof series, book 2 Kindle Edition
by Archimedes Plutonium (Author)

Last revision was 19May2021. This is AP's 11th published book of science.
Preface:
Actually my title is too modest, for the proof that lies within this book makes it the World's First Valid Proof of Fundamental Theorem of Calculus, for in my modesty, I just wanted to emphasis that calculus was geometry and needed a geometry proof. Not being modest, there has never been a valid proof of FTC until AP's 2015 proof. This also implies that only a geometry proof of FTC constitutes a valid proof of FTC.

Calculus needs a geometry proof of Fundamental Theorem of Calculus. But none could ever be obtained in Old Math so long as they had a huge mass of mistakes, errors, fakes and con-artist trickery such as the "limit analysis". To give a Geometry Proof of Fundamental Theorem of Calculus requires math be cleaned-up and cleaned-out of most of math's mistakes and errors. So in a sense, a Geometry FTC proof is a exercise in Consistency of all of Mathematics. In order to prove a FTC geometry proof, requires throwing out the error filled mess of Old Math. Can the Reals be the true numbers of mathematics if the Reals cannot deliver a Geometry proof of FTC? Can the functions that are not polynomial functions allow us to give a Geometry proof of FTC? Can a Coordinate System in 2D have 4 quadrants and still give a Geometry proof of FTC? Can a equation of mathematics with a number that is _not a positive decimal Grid Number_ all alone on the right side of the equation, at all times, allow us to give a Geometry proof of the FTC?

Cover Picture: Is my hand written, one page geometry proof of the Fundamental Theorem of Calculus, the world's first geometry proof of FTC, 2013-2015, by AP.

Length: 137 pages

Product details
ASIN : B07PQTNHMY
Publication date : March 14, 2019
Language : English
File size : 1307 KB
Text-to-Speech : Enabled
Screen Reader : Supported
Enhanced typesetting : Enabled
X-Ray : Not Enabled
Word Wise : Not Enabled
Print length : 137 pages
Lending : Enabled
Amazon Best Sellers Rank: #128,729 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
#2 in 45-Minute Science & Math Short Reads
#134 in Calculus (Books)
#20 in Calculus (Kindle Store)

Preface: 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 question 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, never belonged in science. This then converges with the logic-philosophy of Pragmatism (see AP's book of logic on Pragmatism).

Some of these can be found in AP's TEACHING TRUE MATHEMATICS series, but the entries keep changing and added on new, means I need to have a separate book for these fakes, mistakes and errors of Old Math.

TEACHING TRUE MATHEMATICS: Volume 3 for ages 18-19 Freshperson College, math textbook series, book 3
Teaching True Mathematics, by Archimedes Plutonium 2019
Listing the Errors of Old Math, list of 1 to 50.

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 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, erst, we have no Calculus. So calculus is the consistency maker for the rest of all of mathematics.

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 trashpile 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.

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.