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My historic geometric theorem:
https://drive.google.com/open?id=1RDulODvgncItTe7qNI1d8KTN5bl0aTXj
explains a general formula for any derivative using geometry.
It also proves that both differentiation and integration can be done without any limit theory or other ill-formed concepts such as infinity and infinitesimals:
https://drive.google.com/open?id=1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y
But it's very difficult trying to reeducate dishonest mainstream math academics. They are vile creatures who hate and oppose anyone with different ideas, no matter how good.
My LinkedIn article explains:
https://www.linkedin.com/pulse/how-stupid-mainstream-math-professors-john-gabriel/
A link to the applets used in the video:
Derivative through geometry:
https://drive.google.com/open?id=1ON1GQ7b6UNpZSEEsbG14eAFCPv8p03pv
Fraudulent Calculus:
https://drive.google.com/open?id=14Ua0EPFAUUpNXZXzIdAzXASBqr2yC_wO
Link to article about Lipschitz Condition (Page 118-120):
Link to retired math professor's (Gerry Folland) drivel:
https://sites.math.washington.edu/~folland/Math134/lin-approx.pdf
Links to my battle against the BIG STUPID (mainstream academia):
https://groups.google.com/d/msg/sci.math/MRM9uACbr80/0oZ8IqYxCAAJ
https://groups.google.com/d/msg/sci.math/tNd0WzhXYL0/8PFJOp81AQAJ
Constructive analysis is an excuse for real analysis which is a flawed topic based on an object that doesn't exist - the "real number".
Learn the truth about how we got numbers:
https://www.linkedin.com/pulse/how-we-got-numbers-john-gabriel-1
There is no need for such nonsense and the New Calculus proves neither such analysis is required:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
For centuries academics have not understood many basic concepts. In this video I discuss the concept of area and how it all started.
Subscribe to my BitChute channel:
https://www.bitchute.com/video/rrVK3LyqgI0i/
Link to videos on Area:
https://www.youtube.com/watch?v=tzONfHnxYYI&feature=youtu.be
Link to video on Volume:
https://www.youtube.com/watch?v=mikxfnAYYA0&feature=youtu.be
Link to the applet used:
https://drive.google.com/open?id=1x_8LeAii-_ZZN4CebRVpb09tjfuHlF5M
Download my free eBook:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
NEWS:
About 2 months ago I discovered a geometric theorem that is historic and proves calculus can be done without any limit theory. In fact it proves that limit theory is flawed and a cover up by those who claimed to add rigour to calculus. The theorem explained in this article:
https://drive.google.com/open?id=1RDulODvgncItTe7qNI1d8KTN5bl0aTXj
Not only does this theorem allow you to well define the derivative but also the integral and the connection between the two is seamless!
Read how you can FIX the broken mainstream formulation of calculus in the following article:
https://drive.google.com/open?id=1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y
Spread the news!
Link to the article explaining the theorem:
https://drive.google.com/open?id=1RDulODvgncItTe7qNI1d8KTN5bl0aTXj
Link to article explaining how the theorem fixes the flawed mainstream formulation by removing all ill-formed concepts such as infinity, infinitesimals and the rot of limit theory:
https://drive.google.com/open?id=1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y
Link to download the applet:
https://drive.google.com/open?id=1ON1GQ7b6UNpZSEEsbG14eAFCPv8p03pv
An easy proof of the theorem (you need to refer to the geometry to see what f1 and f2 mean):
We can prove that f'(x) = [f(x+h)-f(x)]/h - Q(x,h) as follows.
Let t(x) be the equation of the tangent line which we don't yet know.
Then [t(x+h)-t(x)]/h = f2/h = f'(x) from the geometry theorem.
This means that f'(x) contains no terms in h because t(x) is a straight line and we know that h is a factor of every term in t(x+h)-t(x).
But f1/h = [f(x+h)-f(x)-f2]/h and so f2/h = [f(x+h)-f(x)]/h - f1/h
Thus, f'(x)= [f(x+h)-f(x)]/h - f1/h which implies that f1/h = Q(x,h).
So, Q(x,h)=[f(x+h)-f(x)]/h - f'(x).
Since the secant line slope [f(x+h)-f(x)]/h contains the sum of f'(x) and Q(x,h), it follows that Q(x,h) has terms with factors of h because f'(x) consists of terms that don't contain h.
An excellent introduction to trigonometry in just 12 minutes.
I dedicate this video to a young friend of mine in the Netherlands who asked which is the best book to learn trigonometry. As the books and methods published by mainstream academics leave much to be desired, I decided to produce this fine video which explains how we got trigonometry.
Link to applet used:
https://drive.google.com/open?id=1i0bE4P3T2vXFET7BHNjpz2jiX8ULcP2j
At 6:30, there is a typo at the bottom where it says: "π/2 =..."
It should simply have "θ=..."
I have corrected this in the applet that has been uploaded.
Old age can be depressing at times. :-)
Link to applet used in demonstration:
https://drive.google.com/open?id=1ON1GQ7b6UNpZSEEsbG14eAFCPv8p03pv
Link to article on Fixing broken mainstream calculus:
https://drive.google.com/open?id=1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y
Link to article describing the historic first rigorous resolution of the tangent line problem:
https://drive.google.com/open?id=1RDulODvgncItTe7qNI1d8KTN5bl0aTXj
Link to my free New Calculus eBook - the first and only rigorous formulation of calculus in human history:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
Note:
You might claim that f1 is being used in the determination of f2, but in geometry this is allowed and it's not circular at all since f(x+h)-f(x) = f1 + f2.
To wit, in geometry we can multiply or divide any magnitude (except for no magnitude of course) EXACTLY. If some magnitude represents pi and another sqrt(2), we can find the exact product pi*sqrt(2) in the form of a magnitude. In algebra this is simply not possible!
The knowledge I share with you in this video is historic. It's monumental. The implications and ramifications are many. This video is about solving the tangent line problem using ONLY geometry which cannot be rubbished. You will be introduced to ONE formula that can be used to calculate ANY derivative of f(x) at x.
1. No need to learn limit theory or real analysis and solid proof that the mainstream formulation of calculus is a kludge based on ill-formed concepts. This knowledge reveals without any doubt that limit theory is neither required in calculus, nor is it rigorous. The mainstream calculus was never rigorous.
2. A rigorous and complete geometric derivation that refutes Cauchy’s ideas about not being able to define the derivative by any means other than algebra.
3. Easy to learn using only high school geometry and trigonometry.
4. No need to learn many differentiation rules and techniques. The ONE formula works on any function. This ingenious idea came to me through my research on how to produce a complete rigorous geometric formulation. The inspiration is to produce a perpendicular from one endpoint of the non-parallel secant line and form similar triangles, thus reducing the problem to one of trigonometry (a specialized geometry of triangles).
My motivation for publishing this FREE information online, is to expose the ignorance of all those who have called me a crank and libeled my upright character. The hatred I possess for them is not described by words. Some of the vilest, most incompetent, most ignorant, arrogant, stupid and jealous academics I have met are from various forums on the internet. Numerous psychopaths have set up web sites about me replete with illogical, libelous nonsense. Some of the most malicious individuals names are listed at the end of my article for good reason: their libel and disparagement of my character has resulted in life altering circumstances: I am homeless, not in the best of health and suffering from severe depression.
Link to article:
https://drive.google.com/open?id=1RDulODvgncItTe7qNI1d8KTN5bl0aTXj
Link to applet:
https://drive.google.com/open?id=1ON1GQ7b6UNpZSEEsbG14eAFCPv8p03pv
I have known this knowledge for several decades, but held back in the hope that I would publish my all time great work "What you had to know in mathematics but your educators could not tell you".
It is now clear to me that this work shall never be published so I reveal this special topic from my book (i) in the name of vengeance against all those moron academics in the mainstream who have libeled me and called me a crank and also (ii) to provoke young students to reject the ill-formed ideas and nonsense taught to them in the mainstream.
There is much, much more I shall never reveal. I am good at keeping secrets. My hope is that every vile academic who has slandered me (and in the process ruined my life) will end up paying dearly for his incompetence, ignorance, arrogance, stupidity and jealousy. Read my latest article to see if a crank can possess such knowledge!
Link to the full article used in the video:
https://drive.google.com/open?id=1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y
Link to my free eBook:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
In this video I show you how to find the derivative using a formula I revealed to the math community just recently.
The article in the video can be downloaded here:
https://drive.google.com/open?id=1E6DdU88Wue5tn2DQAyHZiEB7jeyMGj1q
Unfortunately, it is not that simple to transfer this knowledge over into a method to find the definite integral in the flawed mainstream formulation. But do not despair! It has been done in my New Calculus, the first and only rigorous formulation of calculus in human history. Download my free eBook now!
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
The video explains why there is no valid systematic method of finding the derivative in mainstream calculus and hence the reasons why it is flawed.
Mainstream academics hate nothing more than correction. It exposes their ignorance, incompetence and stupidity.
When they don't like what you have to say, they shun you and then commence on a quest of libel and character assassination. Anyone who doesn't agree with their wrong views is by default a "crank". Very unfortunate.
In this video, I show you how to derive these two geometric objects from nothing. The line is derived from the base notion which is a point. The extended line is derived from the straight line. The circle is derived from the line and extended straight line.
In the next video, I'll show you how to define angle and other circle properties and then prove to you that all right angles are equal - this is the fourth requirement.
All the 5 requirements (NOT axioms) in Euclid's Elements are derived from previous notions beginning with the point which is not derived from any previous notions.
The chapter called "There are no axioms or postulates in mathematics" explains all these things:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
In this video, I show you how to derive these two geometric objects from nothing. The line is derived from the base notion which is a point.
In the next video, I'll show you how to derive the circle.
All the 5 requirements (NOT axioms) in Euclid's Elements are derived from previous notions beginning with the point which is not derived from any previous notions.
The chapter called "There are no axioms or postulates in mathematics" explains all these things:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
A subscriber asked an interesting question about when
one can call a ratio a number and when one cannot.
Well, the Ancient Greeks began with ratios of magnitudes.
A magnitude means the same as size or quantity, but has
not been measured. A number by definition, describes
the measure of a magnitude.
For example, if we have a distance magnitude such as
____, we can say nothing about it until we COMPARE it
to another magnitude, and we do this using the RATIO.
So, if ____ is compared to itself, we know it represents
a ratio and a number - the number is the UNIT.
You can read more about this in my free eBook and watch
any of the many videos I produced on the topic.
Link to my free eBook:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
Also, be sure to read my famous article on How we got number:
https://www.linkedin.com/pulse/how-we-got-numbers-john-gabriel-1
In this video, I show you how to derive these two geometric objects from nothing. The line is derived from the base notion which is a point. The extended line is derived from the straight line. The circle is derived from the line and extended straight line. From the circle, we systematically define angle, arc, etc and arrive at a name for those special angles that are formed when two diameters intersect each other in such a way that the arcs formed are all equal.
In the next video, I'll complete the derivation of the 5th and last requirement.
All the 5 requirements (NOT axioms) in Euclid's Elements are derived from previous notions beginning with the point which is not derived from any previous notions.
The chapter called "There are no axioms or postulates in mathematics" explains all these things:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
In this video, I show you how to derive these two geometric objects from nothing.
The 5th requirement is the least understood of all five. By the stage we complete the first four, we have everything we need, including parallel lines from which we can prove that the sum of angles in a triangle are two right angles. This can be done by symmetry as explained in my free eBook.
The 5th requirement states that the sum of cointerior angles on the same side of a transversal is CONSTANT.
All the 5 requirements (NOT axioms) in Euclid's Elements are derived from previous notions beginning with the point which is not derived from any previous notions.
The chapter called "There are no axioms or postulates in mathematics" explains all these things:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
The video explains the first so called "proof by contradiction" even though the proof is actually based on the absurdity that arises from the initial proposition.
To "assume" means to "suppose to be the case without proof". It does not mean we "believe" it to be true or false as for this matter. The statements which follow "pretend" the initial statement is true.
The IF-THEN deductive logic in mathematics has NOTHING to do with the bullshit of propositional logic which relies on the nonsensical ZFC axioms. For example,
"If the sky is pink then the sun is green" is a true statement in propositional logic. However, in deductive logic in mathematics, the statement IF X THEN Y requires that for Y to be TRUE, X must be TRUE. There is a relation between X and Y.
There are no axioms or postulates in mathematics. Beliefs, decrees and rules have no place in rational thought, only hard, cold (deductive) logic and facts.
Link to applet used in this video:
https://drive.google.com/open?id=1rogFeqIzP75I5XiOPTm9MBPvwMoptwzX
Link to my free eBook:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
The short answer is NOTHING. The bullshit of propositional logic has no relationship with deductive reasoning or logic in mathematics.
IF predicate THEN conclusion in mathematics requires that the predicate be true in order for the conclusion to be true. The predicate is a condition so that the conclusion follows on THIS condition, not any other.
If a predicate is false, then the conclusion may apply to many other statements, but in mathematics we focus on targeted conclusions and we ensure that the predicate is well formed.
Inspiration for this video came from the rot published in the following PDF by one professor of mythmatics at NIU:
http://www.math.niu.edu/~richard/Math101/implies.pdf
Be sure to download my free eBook:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
This video is about understanding what your stupid
math lecturers could never explain to you because
they never understood.
There are many misguided notions about Cauchy sequences
and limits. It is certainly not the case that anything
Cauchy did provided even a modicum of rigour.
The first and only rigorous formulation of calculus is
the New Calculus as described in my free eBook:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
Link to applet used:
https://drive.google.com/open?id=0B-mOEooW03iLZHllZ3A5c3M1dUk
Link to article used:
https://drive.google.com/open?id=1DMLhHHLpeBFlADB8Z9M9bgIj0QIcQB_b
I recently had a run-in a with another prime moron mainstream academic. Watch the video to see how I take the idiot down.
Chuckle.
I will ridicule you without mercy, you baboons! GRRRRRR.
Shut the fuck up you morons!! Know your place!
https://drive.google.com/drive/folders/0B-mOEooW03iLUUlFR0ZwMjNNVjg
The words "construct" and "construction" appear nowhere in the Elements of Euclid. This is important because distances cannot be constructed like tangible objects. The Greeks used these figures or schemata to communicate the ideas behind the diagrams or constructions.
. IS NOT a point or location
____ IS NOT a line
o IS NOT a circle
We use these figures to talk about the concepts of location, shortest distance and the circular path known as a circle with all their special properties.
The Greek word used in the first proposition is "introduce", not "construct". There is an important semantic difference and the Greeks were very meticulous, often omitting half a sentence or even dropping the nouns when the context was clear in their minds.
There is simply no way they would have used the word "introduce" when they had already constructed some of the most complex architecture even by today's standards.
A "distance" cannot be constructed, but it can be introduced and in order to talk about it without actual measure, the geometric figures are used. Much later in the Elements, the concept of measure is introduced.
The least understood book of all is Euclid's Elements. However, this is the foundation of ALL mathematics.
Download my free eBook which explains all these things and much more:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
All you need to do is consider the partial sums:
333... : s(n) = (10^n - 1)/3
999... : s(n) = 10^n - 1
0.999... : s(n)= 1 - 1/10^n
1000... = 999... + 0.999... : s(n) = (10^n - 1) + (1 - 1/10^n)=(10^n - 1/10^n)
So,
333... / 999... = (10^n - 1)/3 -:- (10^n - 1) = 1/3
In the above, we don't even care about n because both 333... and 999... are well defined, so no need for taking any limit. The conclusion is immediately evident.
333... / 1000... = (10^n - 1)/3 -:- (10^n - 1/10^n)
= [1/3 - 1/(3x10^n)] / [1 - 1/10^2n]
In the above, we have to take the limit in order to get 1/3. And why does this happen? Because the limit of 0.999... is 1.
Thus we take limits and we end up with 333... / 999... = 333... / 1000... implying that 9 = 10.
Thanks to Euclid for his brilliant proposition in helping to debunk your delusions. Chuckle.
Tsk, tsk. You can't get any more stupid than this!
Link to sci.math discussion so you can see how many morons still refuse to be corrected:
https://groups.google.com/d/msg/sci.math/szb6MwmmRrY/u-58VOB8DgAJ
Link to applet used in video:
https://drive.google.com/open?id=1jWjsFDY2j-Pb6UJv3O-ePIYT1WiIsbgg
Article which proves 1/3 has no measure in base 10:
https://drive.google.com/open?id=1o5kcWvU35tdt_SY83UFnXZAlsKBAsSYH
Link to my free eBook:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
Euler's worst blunder : S = Lim S
https://www.linkedin.com/pulse/eulers-worst-definition-lim-john-gabriel/
There is a contributor on sci.math called Konyberg who is kindly disposed toward 0.333... and 0.999... as most of you fucking idiots would probably be too. BUT, the objects 333... and 999... which are valid series, produce exactly the same result:
333... : s(n) = (10^n - 1)/3 [A]
999... : s(n) = 10^n - 1 [B]
0.333... : s(n) = (1-10^(-n))/3 [C]
0.999... : s(n) = 1 - 10^(-n) [D]
[B] -:- [A] = 1/3
[D] -:- [C] = 1/3
See? Identical results. Why do you think [A] and [B] are not valid?
Q(x,m,n)=0 is known as the auxiliary equation in the
New Calculus. It is in fact the difference between the
tangent line slope and any parallel secant line slope.
In other words, since the slopes are parallel, the
difference Q(x,m,n) must also be zero.
I explain all the details in this video and show
you how your mainstream equivalent Q(x,h) cannot
be zero which is required and equivalent to what
happens in the flawed first principles method.
In order for Q(x,h) to be 0 which it must be, it is
required that h=0 which is absurb because the expression
f'(x)-Q(x,h) is obtained only after division by h has
taken place.
Link to applet used in video:
https://drive.google.com/open?id=1qfUBsfiEYVCyu-jjYhB8cdI3Eh-k5X0i
Links to discussions terminated on Greek forum:
https://mathematica.gr/forum/viewtopic.php?f=40&t=65174
https://www.mathematica.gr/forum/viewtopic.php?f=9&t=65422
The proof that the New Calculus derivative works for ALL functions is already given on my formal New Calculus site:
http://thenewcalculus.weebly.com
Theory of fractions applet:
https://drive.google.com/open?id=1SyAtoga3Ww9Y7rmGk6vYuwBIY332i9zw
New Calculus Difference Quotient - Example 1 Applet:
https://drive.google.com/open?id=1eeKdyXLDl5m__QfhTfvL0-HEQkk-kETh
New Calculus Difference Quotient - Example 2 Applet:
https://drive.google.com/open?id=1dTX7mT-Q0kkEbuiOkpc-EQotMMZFsVCB
In this video I discuss the sheer intransigence of the mainstream academics which transcends ethnicity.
I recently asked if any Greek were willing to translate my free eBook into Greek and the responses are shown at this link:
https://mathematica.gr/forum/viewtopic.php?f=40&t=65174
https://www.mathematica.gr/forum/viewtopic.php?f=9&t=65422
The hostility, especially from the chief primate Mihalis Lambrou is quite noticeable. He was traveling on the last leg of his journey at Athens airport and instructed his sub-primate "Dimitris" to instantly close the threads.
Given there was only incorrect opinions and assertions with respect to my request for a party interested in translating my work, I decided to post a second comment explaining why f'(x)=f'(x)+Q(x,h) is exactly the same as [f(x+h)-f(x)]/h, which is one of the assertions by the administrators.
This is proved in my video:
Download my free eBook here:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
Remember to click LIKE, become a subscriber and share the NEWS!
The calculus was never made rigorous - not even by a long stretch.
In the following applet, I demonstrate these facts that cannot be refuted:
https://drive.google.com/open?id=1Dx6GTFb-nsOdoJHVeoZWl2DWr-yzHqqR
Mainstream academics are intellectually dishonest and vile creatures. They hate correction and cannot learn new knowledge.
My free eBook:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
The background music is a composition by Kelsey Joanne Rogers who is my niece:
https://www.youtube.com/watch?v=SxzdHj4pYwE
The ultimate truth that dishonest mainstream academics continue to reject is simply this:
[f(x+h)-f(x)]/h = f'(x) + Q(x,h) where Q(x,h)=0 <=> h=0.
is EXACTLY EQUIVALENT to:
f'(x) = Lim_{h->0} [f(x+h)-f(x)]/h
So it is obviously flawed in many respects, not just division by 0, but also circularity wrt limit theory verifinition.
No more IFS, BUTS or anything. I've been telling you this for many decades. It is the truth. The sooner you admit error and change your ways, the better for you.
Created 4 years, 6 months ago.
27 videos
Category None
All my old YT videos are stored here:
https://drive.google.com/open?id=1zk_VX-pyW-uutKmwcs3xxD6w9vx8hza4
What is the New Calculus?
The derivative is found in a systematic way in the New Calculus. There is no systematic way to find the derivative in the bogus mainstream formulation. The method known as "first principles method" is riddled with errors, including illegal arithmetic, ill-formed limit theory and real analysis. In mainstream calculus you need to guess the derivative using the bogus first principles method and then verify it is true using epsilonics arguments.
The definite integral is defined without using any ill-formed concepts in the New Calculus, unlike Riemann's ill-formed definition of the definite integral.
What no mainstream moron has ever been able to understand is what the mean value theorem is all about, yet all calculus works solely because of the mean value theorem.
So what is the New Calculus in one paragraph? The New Calculus is formulated using analytic geometry. No unsound concepts such as infinity, infinitesimals or limits are used. The New Calculus can be learned and mastered by a high school student, without years of useless university courses. But it is much more than just a reformulation - there are new theorems and features not possible using the flawed mainstream calculus. The first you will encounter is the Auxiliary equation. The New Calculus makes sense in every respect. This cannot be said of Newton's bogus calculus whose results are generally true, but the formulation thereof ill formed. Neither Newton nor Leibniz nor anyone who came after them understood calculus as well as I do. In fact, no one in the history of humans has understood calculus as well as I. This may sound cranky but you'll agree once you learn the New Calculus.
Initially students of the New Calculus might be overwhelmed, because it requires a sound knowledge of geometry, algebra and trigonometry - all subjects one studies in high school. A high school student can master the single variable new calculus in just 2-4 weeks.
The first constructive proof of the mean value theorem was produced by me. I am also the first human since Euclid to produce the perfect derivation of number.