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Re: 19/06/2018 #2 of Wikipedia incubator of Archimedes Plutonium < Wp | aki Wp > aki > Archimedes Plutonium

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Borderline between Finite and Infinity[edit]

In early 1990s, Plutonium was trying to make sense of "what are numbers", and infinity, so in that decade of 1990s, he tried to make sense of numbers yet with infinity and explored p-adics, but by 2009, Plutonium realized that to make sense of infinity, requires a borderline between Finite and Infinity, and once he discovered where this borderline was, Plutonium dropped the Adics.

An integer in Plutonium's philosophical view includes objects which have a decimal expansion which never ends. Just as the real number 1/3 can be represented as:

1

3

=

0.33333...

{\displaystyle {1 \over 3}=0.33333...}

the infinite integer whose decimal expansion consists solely of 3s is a valid integer in Plutonium's view:

x

=

.

.

.33333

{\displaystyle x=...33333\,}

This type of number resembles the p-adic integers, but it is different because it is not considered as a convergent sequence, but as a philosophically primitive element of the mathematical universe, an integer. Addition and multiplication are defined digit by digit. Plutonium has two classes of numbers: real numbers which are infinite to the right of the decimal point and finite to the left, and adic integers which are infinite to the left and finite to the right. The two may not be added together.

It is a theorem of Peano Arithmetic that there do not exist integers x,y,z with:

x

3

+

y

3

=

z

3

{\displaystyle x^{3}+y^{3}=z^{3}\,}

but Plutonium claims that this is not a property of adic-integers. Since he believes that the adic-integers are the true integers, he concludes that Fermat's last theorem is false.[8]

Plutonium often states that the set of all integers is uncountable, which in standard mathematical language is an oxymoron. By this statement he usually means that the set of all adic-integers cannot be ordered into a list in the usual way. His proof for this claim is to apply Cantor's diagonal argument. He also sometimes states that there is a direct one-to-one map from the real numbers to the integers, which consists of taking all the digits behind the decimal point and putting them in front.[9] [10]

Adics were only a fleeting stepping stone for Plutonium. To find what the true numbers of mathematics are. And by 2018, Plutonium rejects Adics except to discuss varieties of infinite numbers.

In the 1990s, Plutonium admired these Adic numbers, but around 2009, Plutonium researched into a Infinity borderline, a natural border between Finite Numbers and Infinite Numbers. And soon thereafter Plutonium would no longer admire the Adic numbers for they were just a stepping stone to finding what True Numbers really were. The Adics to Plutonium, after the infinity borderline was found, the adics are fictional-infinite-numbers. Once, AP found the infinity borderline with Finite numbers and so, most of P-adics is dismissed by AP, just a little sliver of Adics is remaining in Logic for AP.

Since the 1990s, AP discovered the Infinity borderline to be 1*10^604 and that changes most all of mathematics. Almost everything in mathematics, that came before, is changed with a concept of a borderline between finite and infinite. Here is a small list of corrections AP found in Mathematics and Logic and is endeavoring to complete a Textbook on mathematics by 2019, titled TEACHING TRUE MATHEMATICS for ages 8 to 26.

Before you do Mathematics, you need to be able to think correctly, straight and clear. Unfortunately schools across the world do not teach proper true Logic. They teach a mish mash gaggle of error filled garbage and call it Logic.

The 4 connectors of Logic are:

1) Equal (equivalence) plus Not (negation) where the two are combined as one 2) And (conjunction) 3) Or (exclusive or) (disjunction) 4) Implication

New Logic

EQUAL/NOT table:

T = T = T

T = not F = T

F = not T = T

F = F = T

Equality must start or begin logic because in the other connectors, we cannot say a result equals something if we do not have equality built already. Now to build equality, it is unary in that T=T and F =F. So we need another unary connector to make equality a binary. Negation is that other connector and when we combine the two we have the above table.

Equality combined with Negation allows us to proceed to build the other three logic connectors.

Now, unfortunately, Logic must start with equality allied with negation and in math what this connector as binary connector ends up being-- is multiplication for math. One would think that the first connector of Logic that must be covered is the connector that ends up being addition of math, not multiplication. But maybe we can find a philosophy-logic answer as to why Logic starts with equal/not and is multiplication rather than addition. That explanation is of course the Space in which the Logic operators govern, and the full space is area, so that is multiplication. And we see that in a geometry diagram

T T

T T where all four small squares are T valued making a 4 square

While addition is and with a Space like this

T T

T F and we have just 3 of the 4 smaller squares covered by addition.

Here you we have one truth table equal/not whose endresult is 4 trues and now we move on to AND as addition.

New Logic

AND

T & T = T

T & F = T

F & T = T

F & F = F

AND is ADD in New Logic, and that makes a whole lot of common sense. AND feels like addition, the joining of parts. And the truth table for AND should be such that if given one true statement in a series of statements then the entire string of statements is true. So if I had P and Q and S and R, I need only one of those to be true to make the string true P & Q & S & R = True if just one statement is true.

The truth table of AND results in 3 trues and 1 false.

New Logic OR(exclusive)

T or T = F

T or F = T

F or T = T

F or F = F

OR is seen as a choice, a pick and choose. So if I had T or T, there is no choice and so it is False. If I had T or F there is a choice and so it is true. Again the same for F or T, but when I have F or F, there is no choice and so it is false. OR in mathematics, because we pick and discard what is not chosen, that OR is seen as subtraction.

OR is a truth table whose endresult is 2 trues, 2 falses.

New Logic IMPLIES (Material Conditional)

IF/THEN MOVES INTO

T -> T = T

T -> F = F

F -> T = U probability outcome

F -> F = U probability outcome

A truth table that has a variable which is neither T or F, but U for unknown or a probability outcome. We need this U so that we can do math where 0 divided into something is not defined.

Now notice there are four truth tables where the endresult is 4 trues, 3 trues with 1 false, 2 trues with 2 falses and finally a truth table with a different variable other than T or F, with variable U. This is important in New Logic that the four primitive connectors, by primitive I mean they are independent of one another so that one cannot be derived by the other three. The four are axioms, independent. And the way you can spot that they are independent is that if you reverse their values so that 4 trues become 4 falses. For AND, reversal would be FFFT instead of TTTF. For OR, a reversal would be TFFT instead of FTTF.

To be independent and not derivable by the other three axioms you need a condition of this:

One Table be 4 of the same One Table be 3 of the same One Table be 2 of the same And to get division by 0 in mathematics, one table with a unknown variable.

So, how did Old Logic get it all so wrong so bad? I think the problem was that in the 1800s when Logic was being discovered, is that the best minds of the time were involved in physics, chemistry, biology and looked upon philosophy and logic as second rate and that second rate minds would propose Old Logic. This history would be from Boole 1854 The Laws of Thought, and Jevons textbook of Elementary Lessons on Logic, 1870. Boole started the Old Logic with the help of Jevons and fostered the wrong muddleheaded idea that OR was ADD, when it truly is AND.

Now the way people actually live, is an indicator of how well they thought and how well any of their ideas should be taken seriously. In the case of Boole, he went to class in a downpour rain, why without a raincoat? And reaching class, instead of changing into dry warm clothes, stood for hours in front of students, sopping wet and shivering. Of course he caught pneumonia, but instead of being sensible, common sense that even a fly would have, he insisted his wife give him cold showers and make the bed all wet and freezing. Of course, he would die from this. Now, does anyone today, think that a mind like that has anything to offer Logic or mathematics, is as crazy as what Boole was.

But once you have textbooks about Logic, it is difficult to correct a mistake because of the money making social network wants to make more money, not go around fixing mistakes. So this nightmarish mistakes of the truth tables was not seen by Frege, by Russell, by Whitehead, by Carnap, by Godel, and by 1908 the symbols and terminology of the Old Logic truth tables were so deeply rooted into Logic, that only a Logical minded person could ever rescue Logic.

1.1 The "and" truth table should be TTTF not what Boole thought TFFF. Only an utter gutter mind of logic would think that in a series of statements, that AND is true when all statements are true, but to the wise person-- he realizes that if just one statement is true, the entire series is true, where we toss aside all the irrelevant and false statements --(much what life itself is-- we pick out the true ones and ignore all the false ones). In fact, in a proof in mathematics, the proof can be full of false and nonsense statements, so long as the proof itself is there and be seen as overall True. For example the proof of SAS in geometry, side angle side, can be packed with false statements and irrelevant statements and still be true. 1.2 The error of "if-then" truth table should be TFUU, not that of TFTT 1.3 The error of "not" and "equal", neither unary, but should be binary 1.4 The error that Reductio Ad Absurdum is a proof method, when it is merely probability-truth, not guaranteed 1.5 The error, the "or" connector is truth table FTTF, never that of TTTF, for the idea of an inclusive "or", --- either A or B or both, is a self contradiction. And funny, how the fathers of Logic-- Boole and Jevons had a connector that was self contradictory, as if the fathers of logic had no logical mind to be doing logic in the first place.

1.6 So that begs the question, what in mathematics has a truth table of TFFF. Well the simple answer is that it is a reverse of TTTF which is AND, and so the former can be got by that of a NOT function on AND. But in isolation, what is a table of TFFF in mathematics? My guess is it is Absolute Value, a form of Absolute Value in mathematics, but that is only a guess, and likely wrong. In 2016 I gave a half hearted argument that TFFF was absolute value.

(2nd Error)

TRUE CORRECT Numbers needed to do Math or any science like physics in particular

Alright, once we have Logic, we start mathematics, and the best place to start is how we recognize and use numbers. Math has two houses, one is Geometry and one is Numbers (Algebra). We can start with either one of them, geometry or numbers. Here we start with numbers.

DECIMAL NUMBER SYSTEM is superior to all other number systems and the only system to be used in SCIENCE, especially physics.

Let us focus on Numbers, how to represent them, for in how to represent numbers can either destroy our understanding or allow us to understand fully and clearly. If we have the wrong representation of numbers, we cannot hope to fully understand them.

In the history of mathematics, one of the key discoveries was the Decimal Number System. It was discovered in Ancient times by Hindu Arabic, but was slowly accepted and needed many changes along the way to our modern day use. But, even as of recently, 2017, most math professors, perhaps all except AP, thought that Number Systems never change the value of numbers, regardless of what system you use. And in the age of computers, the computer electronics favors binary system, with its electronic gate open or closed.

The Binary system is 1, 10, 11, 100, 101, 110, 111, 1000, etc and those represent, 1,2,3,4,5,6,7,8 in decimals.

Trouble is, though, one number system is superior to all other number systems, the decimal system superior. And the representation of numbers, does in fact, affect the values of numbers, except decimal. Decimal Number system is the only system that does not affect the actual true value of the number. How can that be? It is the fractions that are distorted in other number system, not decimal.

The decimal number system is the only non-corrupting system, and all other systems have failures of number values, in the fractions.

The reason Decimal is superior, is because of the 231Pu Atom Totality demands a number system that has Clean-Pure Numbers as border endpoints. A clean-pure number is this progression 1 10 100 1000 10000 etc

and .1 .01 .001 .0001 etc

A clean-pure number is a "1" digit followed by nothing but 0 digits. They make perfect endpoints as borderlines. And Decimal especially highlights clean-pure numbers since it is the use of two primes 2 and 5.

All other number systems have a 10 and 100, etc, but their 10 and 100 is not formed from the two primes 2 and 5.

Why 2 and 5 forming 10 is so special?

It is because all numbers and all geometry comes from the 231Pu Atom Totality. So that pi and 2.71… exist as special because 231 Plutonium has 22 filled subshells in 7 shells and only 19 subshells occupied at any one moment in time, giving 22/7 as pi and simultaneously giving 19/7 as "e".

The final answers as to why why why in science or math, all ends up with a feature of the 231Pu Atom Totality. And the reason for a Number System based on 2x5 is so special is because 231Pu is the 5f6 outer shell and so the 5 comes from that and the 2 comes from 2x3=6.

Did you know in math there is what is called magic-cubes::

If i look at the 231Pu Atom Totality and its 5f6

Then a 3by3 Array, best not call them matrix

Occurs for addition with 5 as center

2 7 6

9 5 1

4 3 8

So the 5f6 hints at trying 6 for center for multiplication

After playing around

18 1 12

4 6 9

3 36 2

For 216 in all rows columns diagonals

Also, interesting is that 216 + 15 = 231 as in 231Pu

The reason that MATHEMATICS even exists, in the first place, is because the Universe just one big atom with smaller atoms inside itself. And since atoms have Shape and Size, thus comes forth the creation of geometry. And since atoms are numerous, many and many atoms, thus is created Numbers, or commonly called Algebra.

The decimal number system is superior and unique to all other number system. Think of it as the "e" of logarithms. The logarithms with base 2.71…. is unique base and is a superior base for any logarithmic system. So the base-10 number system, the decimal system is unique and superior.

Why superior? Well for one, its representation does not corrupt number values. In binary, many numbers as fractions are distorted and corrupted. Not the whole numbers in binary, but once you need to use fractions, often they are distorted in true values.

Here is a recent report of a incident of number value distortion by binary (source stack overflow Internet)

Found this one in stack overflow, bolstering the case i make that all systems except Decimal are crap > >> 50.05/0.05 is not precisely equal to 1001, which it should. >> >> I understand that the above problem arises because all decimal numbers can not be precisely >>written down in binary. But it is very obvious that it will create problem at many places, is there a >>good way to take care of the above apart from rounding off?

You see, what happens in physics when you put all your arithmetic into a computer, especially large number data, and all that number crunching the computer goes through to give you a final answer. An answer that should be .5 not .51, an answer that should be 3.00 not 2.99, an answer that should be 137, not a fraction. An answer that should be 105, 840, 945, not 105.7, 833.--, 939.--. When you use a binary system in science, your math numbers never come out to the correct numbers that Nature has.

So, decimal representation is superior, not only for precision and non-distortion, but because only Decimals can deliver a Grid System in mathematics.

(3rd Error)

A proper Coordinate System is needed, not one in which you have a continuum, rather, one in which you have Discrete Mathematics

Grid Systems were discovered by me, AP, discovered or invented in May of 2013 as I was doing my first edition of a Calculus textbook on the sci.math Internet, and in order to do Calculus, for I needed empty space between consecutive points in Geometry in order to have a integral and derivative. You cannot have a Calculus and have a geometry of a continuum. This meant, I needed to have a Grid System of equally spaced points and empty space between those points, empty space between two consecutive points. You, the reader, will discover for yourself, that the only way you can have equally spaced points with empty space between points is the decimal number system.

There is only ONE Number System that can do a Grid System. Only the Decimal System can mirror reflect small numbers from large numbers and reflect large numbers from small numbers. Let me diagram what a Grid System is and the reader should automatically understand the Grid System.

Integer Grid 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 , 11, 12, etc etc

10 Grid .1, .2, .3, .4, .5, .6, .7, .8, .9, 1.0, 1.1, . . , 9.9, 10.0 with math induction element being .1

100 Grid .01, .02, .03, .04, . . , 99.98, 99.99, 100.00 with math induction element being .01

Only Decimal Number System can do a Grid, because only Decimal Numbers can mirror reflect the small number, the fraction and the large numbers-- whole numbers, and have a math induction element that builds all the numbers in a specific Grid.

Old Math Professors are corrupt in mathematics, for they never change their mistakes, for they never even acknowledge their mistakes, and they keep preaching fake math. They do this because they rather make money selling books of fake math, rather than spend the time to correct fake math. Professors of math are like any other greedy lazy person, get the most money from doing the least amount of work. Old math professors teach that all number systems deliver the same value of any number, and they teach that decimal is no better than binary or ternary etc. True math says that is false; true math says that Decimal System is the only system that delivers true value of numbers and is superior in allowing a Grid System, and all other number systems are junk.

So, here in physics, it matters whether your physics answers of math come from a computer using binary.

Archimedes Plutonium

(4th Error)

Borderline between finite and infinity

Now this mistake in not having a correct Infinity in math, affects the Calculus by a large measure, a large degree. It is impossible to have a correct calculus, when you have a bozo-kook understanding of what is infinity.

This is probably the biggest mistake in all of pure mathematics for it affects all other mathematics. Of course the other sciences, especially physics rarely needs to know what the correct proper infinity is. However, it does show up frequently in the best physics-- quantum electrodynamics, in which it is often used to eliminate infinities that crop up in calculations. This physics math procedure is called Renormalization-- getting rid of the infinities.

The trouble with Old Math, is, well, they were terribly shoddy in logic, in thinking straight and clear. For a logical person, knows, that if you have a concept of finite versus infinite, the only way to handle those two concepts is to realize a border must go between them so that you can tell if any given number is finite or infinite. Otherwise, there is no infinity, if there is no borderline.

There is only one way you can have a concept of finite, by having a concept of infinity, and the only way you can have both, is that a borderline exists between them.

I have pinpointed that borderline from tractrix-circle analysis, from algebraic analysis of algebraic completeness, and from angles of regular polyhedra. The borderline in microinfinity is 1*10^-604 and in macroinfinity is 1*10^604.

The easiest way to see the borderline is to see where pi digits ends in a three zero digits in a row.

3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000

Since the Universe 3rd dimension, one would suspect that where pi digits are there first three digits in a row of 000, that such would be the borderline at infinity.

Now, for physics, that infinity is 1*10^604 for large and 1*10^-604 for the small, makes perfect sense, since in physics, it is extremely, extremely difficult to find anything above 10^200 or smaller than 10^-200, to give the reader a sense of proportion.

If a physicists or other science goes to math for information and knowledge of infinity, well, what they see from mathematics by 2017 is nothing more than just piles of you know what.

(5th Error)

By April 2015, was there for the first time a picture diagram proof of the Fundamental Theorem of Calculus, FTC, not just an analysis argument, but a geometry proof (see below). Old Math could never assemble a picture diagram of the FTC. All they could do is argue with limit concept an analysis argument, never a geometry proof of FTC.

A picture diagram proof of FTC changes all of calculus and thus, changes all of mathematics for it requires a infinity borderline to produce an actual number for the infinitesimal, and that number is the inverse of the infinity borderline. Requiring a infinity borderline to produce the infinitesimal changes all of mathematics, and throwing out the limit concept. By changing all of Calculus and thus correcting mathematics, all of math before 2015 was just trash math.

Picture Diagram needed for Fundamental Theorem of Calculus

Why no continuum and no curves exist in Math, so that the Calculus can exist, and does exist

by Archimedes Plutonium

Calculus is based upon there being Grid points in geometry, no continuum, but actually, empty space between two neighboring points. This is called Discrete geometry, and in physics, this is called Quantum Mechanics. In 10 Grid, the first few numbers are 0, .1, .2, .3, etc. That means there does not exist any number between 0 and .1, no number exists between .1 and .2. Now if you want more precise numbers, you go to a higher Grid like that of 100 Grid where the first few numbers are 0, .01, .02, .03, etc.

Calculus in order to exist at all, needs this empty space between consecutive numbers or successor numbers. It needs that empty space so that the integral of calculus is actually small rectangles whose interior area is not zero. So in 10 Grid, the smallest width of any Calculus rectangle is of width .1. In 100 Grid the smallest width is .01.

But, this revolutionary understanding of Calculus does not stop with the Integral, for having empty space between numbers, means no curves in math exist, but are ever tinier straight-line segments.

It also means, that the Derivative in Calculus is part and parcel of the function graph itself. So that in a function such as y = x^2, the function graph is the derivative at a point. In Old Math, they had the folly and idiocy of a foreign, alien tangent line to a function graph as derivative. In New Math, the derivative is the same as the function graph itself. And, this makes commonsense, utter commonsense, for the derivative is a prediction of the future of the function in question, and no way in the world can a foreign tangent line to a point on the function be able to predict, be able to tell where the future point of that function be. The only predictor of a future point of a function, is the function graph itself.

If the Calculus was done correctly, conceived correctly, then a minimal diagram explains all of Calculus. Old Math never had such a diagram, because Old Math was in total error of what Calculus is, and what Calculus does.

The fundamental picture of all of Calculus are these two of a trapezoid and rectangle. In fact, call the picture, the

FUNDAMENTAL THEOREM OF CALCULUS, Picture

Trapezoid for derivative as the roof-top of the trapezoid, which must be a straight-line segment. If it is curved, you cannot fold it down to form a integral rectangle. And the rectangle for integral as area.

From this: B /| / | A /----| / | | | |____|

The trapezoid roof has to be a straight-line segment (the derivative) so that it can be hinged at A, and swiveled down to form rectangle for integral.

To this:

______ | | | | | |

And the derivative of x= A, above is merely the dy/dx involving points A and B. Thus, it can never be a curve in Calculus. And the AB is part of the function graph itself. No curves exist in mathematics and no continuum exists in mathematics.

In the above we see that CALCULUS needs and requires a diagram in which you can go from derivative to integral, or go from integral to derivative, by simply a hinge down to form a rectangle for area, or a hinge up to form the derivative from a given rectangle.

Why in Old Math could no professor of math ever do the Calculus Diagram? Why? The answer is simple, no-one in Old Math pays attention to Logic, and that no-one in Old Math was required to take formal Logic when they attended school. So a person bereft of Logic, is never going to find mistakes of Logic and think clear and think straight.

by Archimedes Plutonium