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What your ignorant teachers could not tell you - PART 23
Synopsis: The relationship between the arithmetic operators at the foundational level, beginning with the most primitive operator.
A link to the presentation used in this video:
https://drive.google.com/open?id=1AUZ1QKRvThMllO2WXhytOnBxKl-kBSpk
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https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
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https://www.youtube.com/watch?v=B-CFhdGeJnE
A link to the presentation used in this video:
https://drive.google.com/open?id=1AUZ1QKRvThMllO2WXhytOnBxKl-kBSpk
Download the most important mathematics book here free!
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
...
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This number theorem is missed by all the orangutans in mainstream academia. They flatly refuse to acknowledge their ignorance, stupidity and grand incompetence. On sci.math, the morons are fine examples of mainstream academics who refuse to accept truth.
Euler unfortunately defined S=Lim S which led to the nonsense of 0.333...=1/3 and 0.999... = 1 and 3.14159... = pi, etc.
This number theorem tells is clearly that 1/3 has no measure in base 10 and hence cannot be expressed in ANY way in base 10.
Link to the article discussed in the video:
https://drive.google.com/open?id=1o5kcWvU35tdt_SY83UFnXZAlsKBAsSYH
Download the most important mathematics book ever written in human history. I promise you will learn more mathematics than you did in ALL your school and university studies.
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
I am the Great John Gabriel, discoverer of the first and only rigorous formulation of calculus in human history.
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The tangent line was understood correctly by the greats in mathematics. Only today, the infinitely stupid morons of mainstream academia do not understand.
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The link to my brilliant article explaining exactly what is the concept of time:
https://drive.google.com/file/d/0B-mOEooW03iLT1l1Z0hYRy1JaEk
Dumbstein (Einstein) formulated his garbage theories on a concept he clearly did not understand. No theatrical (intentional spelling) physicist I've ever met even has a clue what is the meaning of time. They are unbelievably stupid and gullible.
The fathers of all theatrical physicists (Einstein and Hawking) ensured the ignorance of the last century which continues unabated to this day with special interest groups silencing any opposition to their bogus theories and flawed research.
People, I am a genius. I know whereof I speak. Study my world-class article carefully. You won't find such knowledge in the garbage presented at National Geograhic or TEDX or any of the laughable physics departments at universities worldwide. They are all idiots when compared to my genius.
There are reputable mainstream academics who have much to say about Einstein and his incomprehensible theories:
https://claesjohnsonmathscience.wordpress.com/article/did-einstein-not-understand-math-yvfu3xg7d7wt-70
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Newton, Leibniz and Cauchy were frauds. My discovery of the New Calculus is the first and only rigorous formulation in history.
For this I am called a crank and libeled by fools in abundance.
There is a price this generation will pay. I shall not share the best of my discoveries and history will vindicate me.
I loathe modern academic bastards with a passion - they are ignorant, unbelievably stupid, jealous and outright failures. None of them had the intelligence to realise what I have. None of them even got close.
1. There is an error at 0:27.
-9/12 is proportional to -3/4 and so,
-9/12 = -3/4 = - [9 -3-3-3]/[12-4-4-4] = 0/0
I could also have written it like this:
-9/12 = 3/(-4) = (9-3-3-3)/(-12+4+4+4)=0/0
In my video, p ~ m (read as: p is proportional to m) and q ~ n.
The unknown theorem states:
Given any number p/q, there exists another number m/n equivalent to p/q such that a finite number of operations (p+m) / (q+n) or (p-m) / (q-n) will result in a meaningless fraction 0/0.
2. I used the word *proportional* in my video, instead of *equivalent*, but the latter is the correct word and the meaning intended. Any one with a modicum of brains would have inferred this.
Being a polyglot (Greek is one of them!) can sometimes lead to silly mistakes like this. Ultimately, the meaning is clear and only those argumentative fools will harp on semantics rather than examine the truth that destroys ALL their calculus foundations.
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Proposition 13.
᾿Εαν τέσσαρες αριθμοί ανάλογον ώσιν, καί έναλλαξ ανάλογον έσονται.
Heath: If four numbers are proportional then they will also be proportional alternately.
Heath remarks:
In modern notation, this proposition states that if a : b :: c : d then a : c :: b : d, where all symbols denote numbers.
Not only the above proportion, but also
b : a :: d : c
c : a :: d : b
a : c :: a+c : b+d
etc.
So what we observe in Book VII are most of the algebraic operations that are transferred from Book V.
Propositions 14 and 15 are unremarkable and have been covered in Book 5.
Proposition 16.
Εάν δύο αριθμοί πολλαπλασιάσαντες άλληλους ποιώσί τινας, οί γενόμενοι εξ αυτών ίσοι άλληλοις έσονται.
Heath: If two numbers multiplying one another make some (numbers) then the (numbers) generated from them will be equal to one another.
Heath Remarks:
In modern notation, this proposition states that a b = b a, where all symbols denote numbers.
It was proved in Book 5 that multiplication is a reciprocal measure of division using the measure of ratios, that is,
p ×q is possible if and only if p ÷ 1/q=q ÷ 1/p .
Refresher example: 5×3:
p ÷ 1/q=5 ÷ 1/3=5/1/3=5+5+5/1/3+1/3+1/3=15/1=15
q ÷ 1/p=3 ÷ 1/5=3/1/5=3+3+3+3+3/1/5+1/5+1/5+1/5+1/5=15/1=15
In the above example, the abstract unit is the standard of measure as opposed to the consequent of a ratio. Observe also that the denominator is always divided into equal parts.
So in conclusion,
5×3=5 ÷ 1/3=3×5=3 ÷ 1/5
Once again, if either p or q is 0 in p×q, then multiplication is not possible. Zero cannot be divided into equal parts or in any other way.
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Book VII, Def. 1:
Μονάς ἐστιν, καθ᾿ ἣν ἕκαστον τῶν ὄντων ἓν λέγεται.
A unit is (that) according to which each existing (thing) is said (to be) one.
Revised Elements Definition of Abstract Unit (unpublished):
The Abstract unit is the measure of a ratio of magnitudes (preferably line segments) whose aliquot parts are equal and chosen as a standard of measure.
Mathematics is the ABSTRACT science of MEASURE and NUMBER.
A MEASURE is primitively a qualitative process that compares two magnitudes if it can be certain they are different. The process returns shorter or longer but not how much shorter or longer.
The requirements are not axioms:
https://www.academia.edu/45567545/There_are_no_postulates_or_axioms_in_Greek_mathematics
A number is a NAME given to a MEASURE of a RATIO of MAGNITUDES.
Theory of fractions from Book V:
https://www.academia.edu/69488136/Theory_of_fractions_from_Book_5_of_Elements_for_Dummies
Symmetry of the circle defines four basic operations of arithmetic (- + -:- x):
https://www.youtube.com/watch?v=o_KadhQKKfg
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This video is for those who want to know a little more about me.
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Definition 4.
Λόγον έχειν πρός 'αλληλα μεγέθη λέγεται, α δύναται ολλαπλασιαζόμενα αλλήλων υπερέχειν.
(Those) magnitudes are said to have a ratio with respect to one another which, being multiplied, are capable of exceeding one another.
Of all the definitions in Euclid’s Elements, I have always found this one to be the most problematic in terms of understanding. I do not agree with Thomas Heath’s interpretation or anyone else’s that I have come to know.
Perhaps the most laughable interpretation is the one by cranky Prof. David Joyce of Clark University:
"This definition limits the existence of ratios to comparable magnitudes of the same kind where comparable means each, when multiplied, can exceed the other. The ratio doesn’t exist when one magnitude is so small or the other so large that no multiple of the one can exceed the other. This definition excludes the ratio of a finite straight line to an infinite straight line and the ratio of an infinitesimal straight line, should any exist, to a finite straight line." - David Joyce
The Ancient Greeks rejected any ill-formed concept such as infinity and infinitesimal. Moreover, the only objects that were recognised to be numbers by the Ancient Greeks were the rational numbers. Irrational magnitudes were never called (or understood to be) numbers of any kind.
Here’s my interpretation:
Magnitudes in such a ratio, will when multiplied with each other, exceed the original magnitudes. Such magnitudes are greater than the chosen or standard magnitude of measure.
Simple version: Euclid is talking about magnitudes greater than the lowest common divisor or the unit magnitude (whatever it might be) in the process of measure. For example, the magnitudes 2/10 and 8/10 do not qualify since their product 4/25 is less than both 2/10 and 8/10. Also, 0.8 and 3 have a product of 2.4 meaning that neither 0.8 nor 3 are in such a ratio.
“Whoa!”, you may say, “Mr. Gabriel, what you used are numbers but magnitudes are not numbers.”
You would be right, except that I am speaking in the context of a chosen or standard magnitude of measure. I only used numbers to more easily illustrate the fact. Multiplication in geometry only uses magnitudes.
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Synopsis: Time is a special kind of ratio and is formulated using distance. In particular, we formulate our time on the earth's standard repeatable motion, but one can define time on any other standard repeatable motion. To learn much more, read my detailed article on LinkedIn:
https://www.linkedin.com/pulse/what-time-john-gabriel
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