In order for any of the methods of calculus to apply at all, a given function must be both continuous and smooth. This video explains in very simple terms what both these concepts mean.
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https://www.youtube.com/watch?v=lYBcPWJ8kIo
I have many enemies. For years I have been persecuted, lied about, libeled and defamed.
Most of the rot you'll read on the internet falls into one of the following categories:
1. Name calling: I am called a crank, crackpot, psychopath, etc.
2. Lies and Libel: There are many untrue claims about me, my work and life. For many years there has been a concerted effort by mainstream academic scum to systematically assassinate my character and permanently destroy my life.
3. Pretend disproof of my work: These sites are either devoid of mathematics or simply irrelevant because if there are any facts, the same do not disprove anything wrt my New Calculus.
People, do not just believe in all the rot you find on Google searches. Think and judge righteously. I have NEVER been in trouble with the law in any of the many countries where I have lived and worked.
I'll say again: I have never been arrested or charged or even detained. I am whiter than snow! Cleaner than anyone else I know in spite of the fact that many have tried to dig up dirt on me. You can try but you will fail!
I speak with authority because I am smarter than anyone I know. Wrt mathematics, I can't think of any other person who has my depth of understanding. This is not arrogance. It's fact. I am proud (not arrogant!) of my work and what I have accomplished. My numerous enemies are pathologically jealous, hateful and vengeful.
Don't mudsling on the internet under an alias or in any other way. Your actions can and do have devastating consequences not only for me but for the millions who can still benefit from my knowledge.
Use your brain!
The Big Lie: "Calculus was made rigorous...":
https://drive.google.com/file/d/1peL7lzXsmZ4AVsgAwDLvn8QIZbWy8Ebm
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https://www.youtube.com/watch?v=YtLFqlrLUf4
The methods of calculus only apply to smooth functions. My intellectual inferiors in the mainstream mathematics community (all of them mental midgets compared to me) have never understood calculus or the reasons why it works. To wit, the clowns think that "limit theory" is at the core of calculus and the reasons it works - this is FALSE.
In this video, I chose a question by one of my viewers (Chaos Jumper) to explain why it is that we can find area which I have generally defined as the product of two arithmetic means.
No one can gain a profound understanding of calculus without me. I am truly the greatest mathematician and math educator alive today - scorned and hated by the mainstream community because I expose their grand ignorance, incompetence, stupidity and pathological jealousy. They have destroyed my life, but you shouldn't let them destroy yours. The evil reptiles have made it impossible for me to gain the recognition I so rightly deserve. You can change this, not for my benefit, but for yours!
Mainstream math academia is a corrupt cabal, neither interested in truth or new knowledge outside their cultish circle. The Church of Academia (mainstream math academics) is a RELIGION, no longer interested in learning and much less truth.
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https://www.youtube.com/watch?v=CncrJjEAbyA
No matter what you try to do with the bullshit of mainstream calculus theory, it is broken beyond repair. Don't waste your time studying garbage but rather study my New Calculus, the first and only rigorous formulation of calculus in human history.
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https://www.youtube.com/watch?v=lFNff2mpW9Q
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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https://www.youtube.com/watch?v=cSKHOxbDxYQ
Complex numbers are not numbers, but quasi-number objects. All mathematics is possible without complex number theory, including Fourier Series.
A complex number is an ill-formed concept.
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https://www.youtube.com/watch?v=LD-Oz2KMjm0
The most important definition of Book 5 which was never understood by any mainstream mathematics academic. In fact, not even understood by modern Greek math academics!
Definition 3:
Λόγος εστί δύο μεγεθών ομογενών ή κατά πηλικότητα ποια σχέσις.
A ratio is composed of two homogenous magnitudes with respect to how each magnitude might measure the other.
The Greek word πηλικό means quotient. πηλικότητα means “quotientness”. In other words, a ratio is simply the comparison of two random magnitudes p and q denoted by p : q and how each and/or parts of each might measure the other. The comparison is purely qualitative, not quantitative as number is only introduced in Book 7 through the abstract unit.
p : q literally means "p compared with q"
What interests intelligent people, is do these have a relationship? That is, do they have quotientness? In simple words, do they have a common divisor. If they do, then we can proceed to call the measure by the number by the name p/q, which DOES NOT mean "p divided by q".
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https://www.youtube.com/watch?v=2ZDrEPj0A00
The video explains what is a differential in calculus and also a ratio of differentials (derivative). Differentials and derivatives (fractions of differentials) are manipulated exactly like numbers. My intellectual inferiors in the mainstream have never understood calculus. I, the great John Gabriel reveal these things to you.
Download the most important mathematics book ever written here:
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
It's free because it is priceless.
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https://www.youtube.com/watch?v=wg-hsXQh4TY
Leonhard Euler was one of the preeminent mainstream mathematics cranks. It was Euler who defined in his Elements of Al-gibberish (Algebra?) that S = Lim S.
https://drive.google.com/file/d/12oUJAfIMFMcXFb8DvgsYxuPfdaB99XYH
Link to sci.math discussion mentioned in the video:
https://groups.google.com/g/sci.math/c/4XuGLMwWCXI/m/jVeNMIflBQAJ
A mainstream math crank is a member of the mainstream math community who cannot be convinced of his/her error even in the face of overwhelming evidence.
About 30 years ago, an interesting research project was conducted SOLELY on mainstream academics with a view to learning why facts do not change their minds. One of the results is that they suffer from confirmation bias. The article link follows below:
www.newyorker.com/magazine/2017/02/27/why-facts-dont-change-our-minds
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https://www.youtube.com/watch?v=44llMqnBSGg