SEE PICTURE DIAGRAM of FUNDAMENTAL THEOREM OF CALCULUS below, professors hate teaching this for it shows their "limit calculus to be a joke"
PICTURE DIAGRAM OF FUNDAMENTAL THEOREM OF CALCULUS
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.
______ | | | | | | ---------
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 ------------------ -------------------
On Wednesday, January 3, 2018 at 5:08:51 PM UTC-6, burs...@gmail.com wrote: > AP brain farto, can also fart through is belly. > NNTP-Posting-Host: 188.8.131.52 From: burs...@gmail.com > Here have a banana AP brain farto: >
That is all Burse ever talks about, is that a normal Swiss? Maybe Switzerland needs a change of name from Switzerland to Fartland.
Drs.Wendelin Werner Klaus Ensslin Drs.Emmanuel Kowalski, Urs Lang DRs.Tristan Riviere, Dietmar Salamon Drs.Michael Struwe, Benjamin Sudakov-- Zurich ETH, are you as dumb in Calculus, no Picture of Fundamental Theorem of Calculus, as is math failure Jan Burse?? Drs.Kurt Wuthrich,Daniel Vassella Univ Bern, are you as dumb in Calculus, never a Fundamental Theorem of Calculus diagram, as is math failure Jan Burse??
Jan Burse is not only a failure of math, --must have have been burnt out at school-- but also an insane crank on sci.math for 4 years now. I have often asked Google to please engineer a delete key so original authors of a thread can develop their own thread without these insane stalking poopers pooping up (Jan is a 4 year stalker). Let original authors delete any post in their thread which is unfit. Let insane stalkers make their own threads so they can crap all they wish without interrupting those doing serious science.
MAKE sci.math a Level Playing field, and stop tilting sci.math in favor of moron stalkers. -----------------------
Paul Biran Marc Burger Patrick Cheridito Manfred Einsiedler
Paul Embrechts Giovanni Felder Alessio Figalli Norbert Hungerbuhler Tom Ilmanen Horst Knorrer Emmanuel Kowalski Urs Lang Rahul Pandharipande Richard Pink Tristan Riviere Dietmar Salamon Martin Schweizer Mete Soner Michael Struwe Benjamin Sudakov Alain Sznitman Josef Teichmann Wendelin Werner Thomas Willwacher
Zurich ETH, physics dept Charalampos Anastasiou, Niklas Beisert, Adrian Biland, Gianni Blatter, Marcella Carollo, Christian Degen, Leonardo Degiorgi, Gunther Dissertori, Klaus Ensslin, Tilman Esslinger, Jerome Faist, Matthias Gaberdiel, Aude Gehrmann-De Ridder, Vadim Geshkenbein, Christophorus Grab, Michele Graf, Jonathan Home, Roland Horisberger, Sebastian Huber, Thomas Markus Ihn, Atac Imamoglu, Steven Johnson, Ursula Keller, Klaus Kirch, Simon Lilly, Joel Mesot, Renatto Renner, Andre Rubbia, Werner Schmutz, Thomas Schulthess, Manfred Sigrist, Hans-Arno Synal, Matthias Troyer, Andreas Vaterlaus, Rainer Wallny, Andreas Wallraff, Werner Wegscheider, Audrey Zheludev, Oded Zilberberg
University Bern Christian Leumann Walter Benjamin Emil Theodor Kocher Kurt Wuthrich Friedrich Durrenmatt Daniel Vassella Rene Fasel Mani Matter
/\-------/\ \::O:::O::/ (::_ ^ _::) \_`-----'_/ You mean the classroom is the world, not just my cubbyhole in Switzerland?
And, even though you-- professors of math, want to remain stupid in Calculus, your students deserve better.