Be very careful to believe that any published knowledge is reliable. No one can think for you and there is no such thing as "reliable mainstream knowledge". It's a pipe dream conjured up by the mainstream church of math academia and its vile priests.
Be careful of many references and links. Also, be careful of writers referencing their own publications!
To survive in the Babylon of mainstream math academia, you need to be as subtle as a serpent and harmless as a dove. Mainstream mathematics academia is a cult - just as fundamentalist and even more so than many religious cults. You will be dealing with arrogant, incorrigibly stupid people who have less worth than dog excrement. Somehow you have to navigate past these obstacles and the way to do this, is to think for yourself! Be an independent thinker!
Don't fall for the all-time lie that geometry relies on axioms:
https://www.academia.edu/45567545/There_are_no_postulates_or_axioms_in_Greek_mathematics
The greatest book ever written on the subject of numbers:
https://www.academia.edu/105399167/The_Ultimate_Book_of_Numbers
Greeks could perform measure to 100% accuracy even before number concept which comes from geometry:
https://youtu.be/o_KadhQKKfg
Theory of fractions and arithmetic from Book V of Euclid's Elements which mainstream math academics were too stupid and incompetent to understand:
https://www.academia.edu/69488136/Theory_of_fractions_from_Book_5_of_Elements_for_Dummies
Become a follower on Academia.edu:
https://independent.academia.edu/JohnGabriel30
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https://www.youtube.com/watch?v=bchb7pAC37I
There are always some cranks who are more vicious than others. Two such cranks are Jean Pierre Messager and Markus Klyver, both spew out their ignorance on sci.math (see links below).
The Historic Geometric Theorem proves that neither Newton, nor Leibniz nor any other mainstream academic before me actually solved the tangent line and area problem rigorously. I, John Gabriel, was the first to accomplish this because the historic geometric theorem of January 2020 was realised from the New Calculus, which is the first rigorous formulation of calculus in human history:
https://www.academia.edu/41616655/An_Introduction_to_the_Single_Variable_New_Calculus
Article Link:
https://www.academia.edu/104346112/Many_Abel_Prize_Laureates_but_not_a_single_one_with_any_worthwhile_contribution
Applet Link:
https://drive.google.com/file/d/1Po2IAXsG9txLuCs41vDsXgLv2_TsTCJ8
Links to libelous bullshit on sci.math:
https://groups.google.com/g/sci.math/c/NYPVbXdYh7E
https://groups.google.com/g/sci.math/c/iurNOudlGg8
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https://www.youtube.com/watch?v=dCIbByi9A8M
How can mainstream mathematics academics still deny the truth of the Holy Grail of Calculus (HGC)?
The HGC tells us the derivative is not some imaginary rise/run which we guess as a limit and then prove it's true, all the while knowing there is no finite difference ratio dy/dx in terms of f such that f'(x)=dy/dx which self-destructs as the one end point of the non-parallel secant line gets close to the point of tangency. The HGC tells us the exact ratio dy/dx. No hand-waving, no 6-month course on the bullshit of limits, real analysis, etc.
The HGC tells us that the integral is not some imaginary infinite sum which self-destructs to zero area as the rectangles get too thin. The HGC tells us the integral is a product of platlyks (level magnitudes).
They deny these truths because accepting them and admitting error is an existential threat to them. They are pathologically jealous because they were not able to solve these problems and someone outside of their sewer echo chamber revealed the Holy Grail - a simple geometrical truth that cannot be refuted - not even by the "gods". More advanced alien civilisations would be laughing if they knew of the ridiculous mainstream formulation of calculus.
One more thing that astounds me: Engineers and architects are the ones using calculus the most and in some respects they are more fanatical about limits than the orangutans who built their job security there upon. I have to say though that most engineers and architects agree with me - this is at least one good thing. Only the lackeys and sycophants do not stray from mainstream doctrine.
The entire Church of Mainstream Mathematics Academia is a cesspool full of hurt anuses, revisionists, sexual deviants and just plain intellectual stupids.
The Holy Grail of Calculus (worth more than one Abel prize!):
https://www.academia.edu/105576431/The_Holy_Grail_of_Calculus
The Ultimate Book of Numbers:
https://www.academia.edu/105399167/The_Ultimate_Book_of_Numbers
Proof of the Historic Geometry Theorem:
https://www.academia.edu/62358358/My_historic_geometric_theorem_of_January_2020
Become a follower of Academia.edu:
https://independent.academia.edu/JohnGabriel30
Donate here:
https://gofund.me/af8a5312
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...
https://www.youtube.com/watch?v=ZtYeF2PcX2I
Mainstream academics are incorrigibly stupid. They will not listen to reason or accept valid proofs.
Do you want to remain an idiot? If not, learn the New Calculus, the first and only rigorous formulation in human history.
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https://www.youtube.com/watch?v=OMGkW_4A9M8
The first ever neusis was done by what I call a "tangemeter" - a straight edge that hugs a given curve with the result that only one point of the curve and straight edge are ever in contact. Neusis has been misunderstood by all the academics I have ever spoken to. Archimedes used it effectively and Euclid abandoned it, choosing to accept the definition of tangent line as given by his predecessors: a finite line meeting any curve in only one point and crossing it nowhere.
The only modern theorem and the most important one in calculus, the mean value theorem can be stated as follows:
The tangent line slope at one or more points in an interval equals to the arithmetic mean of all the derivative function y ordinates.
The mean value theorem does not care about inflection points because there is no tangent line by definition, at points of inflection.
Neusis was never considered to be rigorous because the concepts of geometry are abstract and the use of compass or straight edge are only for communicating the perfect ideas.
Link to applet used in this video:
https://drive.google.com/file/d/1Hk9W6yQK0JGIuFp7GvvVHRyn8EFN0fnh
Old video about Trisectrix:
https://www.youtube.com/watch?v=ltKHED5kcUk
After listening to this video, I realise that I made a few mistakes but none that will affect the main message. :)) I am getting old... sigh.
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https://www.youtube.com/watch?v=VVVRwaoIlgI
Want to understand number better than any past mathematician or mathematics professor or teacher? Your only hope is in my free eBook:
https://www.academia.edu/105399167/The_Ultimate_Book_of_Numbers
Don't waste your time on bullshit such as the "Access Problem" or other "philosophical writings" that say a lot about nothing.
Mathematics is the ABSTRACT SCIENCE of measure and number.
Become a follower on Academia.edu:
https://independent.academia.edu/JohnGabriel30
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https://www.youtube.com/watch?v=l7LrADDW1QQ
The so-called Intermediate Value "Theorem" (IVT) is not a theorem at all, but a plain self-evident truth. Mainstream mathematics educators who are absolute morons try to prove the IVT using the garbage of set theory, but it turns out that the "proof" is just more of their hand waving spoofs so common throughout their worthless textbooks. They love to wax eloquent by stating obvious facts in the form of set theory and inequalities and then trying to disguise the same as "proofs". The hilarious part is that they usually move from the IVT to the theorem known as Rolle's Theorem (also very self-evident and not worthy of being called a theorem) and finally they use Rolle's in an attempt to prove the Mean Value theorem which the morons have never understood!
Link to article used in presentation:
https://www.academia.edu/88426311/The_utter_nonsense_known_as_the_Intermediate_Value_Theorem
Thank me for enlightening you by contributing here:
https://gofund.me/af8a5312
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https://www.youtube.com/watch?v=lQnqlTm4sGY
This video covers propositions 17 through 20 of Book 1 of Euclid's Elements.
Link to applet used in this video:
https://drive.google.com/file/d/16CG7NCJmXpGaWz96BIRNmf9vY-J4jGan
Prologue to Euclid's Elements:
https://youtu.be/u_hmoVZNFn8
Lecture on the 5 requirements:
https://youtu.be/_WZJY1xgJTk
Link to applet used in video:
https://drive.google.com/file/d/1p5oRcbHOiM6WJFpMwDfzkLb0s0yM-Jeg
. IS NOT a point
____ IS NOT a line
o IS NOT a circle
The de facto foundations of mathematics are Euclid's Elements, not the rot known as ZFC axioms and set theory. Everything we know about science is derived from the Elements without any exception.
I quote a Greek scholar (http://www.physics.ntua.gr/mourmouras/euclid/common/anti_prologou.html):
Τα Στοιχεία Ευκλείδου δέν είναι Γεωμετρία (ούτε επιπεδομετρία, ούτε γεωμετρία χώρου), απλώς μπορούν να παραχθούν από αύτα «Γεωμετρίες» (είτε «Ευκλείδειες,» είτε «μή Ευκλείδειες», κλπ), όπως επίσης μπορούν να παραχθούν πολλές άλλες θεωρίες «Μαθηματικές» καί όχι μόνο, π.χ. Θεωρία Αριθμών, Aναλογίες, Aσύμμετρα Μεγέθη, Θεωρία της Σχετικότητας, κ.α.
Τα Στοιχεία τού Ευκλείδου δεν είναι ούτε αντικείμενα του Πραγματικού κόσμου, καίούτε είναι αντικείμενα τών Μαθηματικών, αλλά χωρίς αυτά, όλα τά παραπάνω δέν μπορούν να περιγραφούν, να κατανοηθούν, να ερμηνευτούν.
Πολλοί συγχέουν τον πραγματικό χώρο τών «Φυσικών» επιστημών με τά Στοιχεία Ευκλείδου. Aπό τα Στοιχεία Ευκλείδου προέρχονται οί πλείστες μαθηματικές καί φυσικές επιστήμες, τόσο οί παραδοσιακές όσο καί οί μοντέρνες. Γιά τις τεχνολογίες αυτό είναι προφανές.
Τα Στοιχεία Ευκλείδου αποτελούν ένα ενιαίον όλο, ένα «Σύστημα», τό οποίο είναι «κλειστό καί ἀνοικτό», τόσο όσο καί ή σκέψη, ό λόγος καί ή γραμματική τής ανθρώπινης υπόστασης. H πληρότητα καί ἡ συνέπεια είναι δομημένες μέ έναν εκπληκτικό τρόπο, πού τό καθιστούν μοναδικό.
My καθαρεύουσ�
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https://www.youtube.com/watch?v=zPReD6fR6iA
Synopsis: The seventh belief is the axiom of replacement required so that moronic set theorists can formalise their definition of function.
It fails easily as the video example shows.
Download the most important mathematics book ever written here - it's free!
https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
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https://www.youtube.com/watch?v=D12lfFtMO18