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Re: Fundamental Theorem of Calculus is superfluous in New Math #9 TRUE CALCULUS; without the phony limit concept (textbook 1st ed.)
Posted:
May 21, 2013 4:55 PM


On May 21,2013, Archimedes Plutonium wrote: > Alright, I have come to some decisions at this stage of this tiny > > textbook, that I shall make it no longer than 10 pages. I decided on > > that because a bright Middle School student can handle 10 pages of > > mathematics that he or she has never seen before and learn something. > > However if 25 pages, they would likely be too discouraged. And also, > > because True Calculus has no limit concept, that most of modern day > > calculus of those 700 page texts, much of that gobbleygook phony > > baloney or gibberish nattering nutter speak is about the limit. When > > you have true math, you need just 10 pages to explain it. When you > > have fake math, you need 700 pages of symbolism and abstractions to > > hide and cover up. > > > > So I have two pages remaining in this edition. And when I do the 2nd > > edition I can do it all in two days posting 5 posts per day. So a > > rapid fire book is this, because I can have the 100th edition within > > one year. > > > > Now since this text is only 10 pages long, I need no chapters to > > organize because from start to finish, anyone can read it in one day > > and no point in dividing 10 pages into chapters. > > > > Now let me outline the education system of how calculus is taught in > > Old Math. The first Calculus in the school system is called > > "Precalculus" and it teaches about function, about area under graph > > and about slope and tangents, but stops short of the limit concept. > > Calculus taught in College is basically a year study of the "limit > > concept". So in Old Math, calculus and limit concept were one and the > > same. > > > > In New Math, we start first with the concept of finite moving into > > infinity and have to find a borderline of where is the last finite > > number and the start of infinity. I found that borderline to be Floor > > pi*10^603 where pi has three zero digits in a row and is evenly > > divisible by 2,3,4,5 or 120. This divisibility is important for it > > gives us the Euler regular polyhedra formula and it gives us where the > > surface area of the pseudosphere equals the area of the corresponding > > sphere. The inverse of that infinity borderline I denote as 1*10^603 > > is the smallest nonzero number possible in mathematics and geometry. > > It is the metric size of the hole or gap or empty space between 0 and > > the next number which is 1*10^603 and the next number after that is > > 2*10^603 and there are no numbers in between those three numbers > > listed. There is just empty space, however one can draw a line or line > > segment in that empty space even though there are no number points. > > > > So these holes and gaps make the limit concept as fictional, for there > > is no need of a limit. The holes themselves serve as a limit. The > > holes prevent pathological functions from forming such as the > > Weierstrass function or the function y = sin(1/x). > > > > The holes allow the derivative to form or come into existence because > > the hole gives the derivative room to form a angle, an angle between 0 > > and 90 degrees. Without the hole or empty space, the neighboring > > infinite points would obstruct as in the Weierstrass function, > > obstruct the formation of the derivative. But since every point in the > > Cartesian Coordinate System is surrounded by a hole of at least > > 10^603, that every point of the function is differentiable. > > > > The holes allow the integral to come into existence because with the > > empty space the integral is a summation of very thin picketfence > > rectangles with a triangle on top of the rectangle. The hypotenuse of > > the triangle top is the derivative. The integral is the summation of > > all these picketfences whose width is exactly 10^603. In Old Math, > > the integral was a summation of line segments, but even Middle School > > children have learned that lines and line segments have no area, yet > > calculus professors seem to have lost sight of the fact that line > > segments have no area when they explain calculus. So the hole of > > 10^603 allows the integral to form and exist. > > > > Now in most Old Math calculus texts of those 700 page gibbering > > nattering nutter symbolism of limits, once they cover derivative and > > integral, they usually want to tie the two together in what is called > > the "Fundamental Theorem of Calculus". And they make a big stir and > > fuss about this. But in New Math, we not only throw out the limit as > > fakery, but we have no need to show that the derivative is the inverse > > of integral and vice versa. In mathematics, do we need to have a > > Fundamental theorem of add subtract or a Fundamental theorem of > > multiply divide and prove they are inverses? No, we need not go > > through that silliness. > > > > In New Math, in True Calculus we merely note that the derivative is > > the angle of the hypotenuse atop the picketfence which determines a > > unique area of the picketfence, so that the derivative is the inverse > > of the integral. If I change the area of the picketfence, I change the > > derivative proportional to the area. If I change the angle of the > > hypotenuse, I proportionally change the area inside the picketfence. > > > > So in True Calculus we throw out the phony baloney limit concept and > > along with it we have no need for a hyped up exaggerated Fundamental > > theorem. > > > > Now let me speak more about geometry, since I have just these 2 last > > pages. It is important to know the relationship of geometry to numbers > > and that should have been the Fundamental Theorem of Calculus. The > > fundamental theorem should have embodied the idea that why the > > Calculus exists at all is because in Euclidean Geometry when we have a > > Cartesian Coordinate System of dots separated by 10^603 holes, that > > no matter what the size of the graph is, the relationships of where > > those dots are to each other always forms the same angles. So that the > > function y= x is always a 45 degree angle. So the Fundamental Theorem > > of Calculus should have been a theorem that explores and proves why > > Euclidean Geometry can yield a calculus but that Elliptic geometry or > > Hyperbolic geometry cannot yield a calculus. > > > > And another geometry feature I want to start to explore is a truncated > > Cartesian Coordinate System. > > Here I have just two points for the xaxis of 0 and 1*10^603 and I > > have all the points of the yaxis from 0 to 10^603 or 10^1206 points > > in all. Now I call that a truncated Coordinate System of the 1st > > quadrant. And you maybe surprized as to how much one can learn from > > this truncated system. It has the functions of y=3, and y=x, and > > y=x^2. It also has the functions of Weierstrass function and the > > function y = sin(1/x). > > > > So for the function y=3 we plot the point (0,3) and (1*10^603, 3). It > > has the function y=x and we plot the point (0,0) and (1*10^603, > > 1*10^603). > > > > What is nice about the truncatedCoordinate System is that we can > > instantly learn a lot about functions without being bogged down with > > distractions of a lot of point plotting. We can home in on just the > > derivative or integral in that truncated interval and we can see how > > in New Math, all the points and numbers of mathematics should be > > transparent and visible to the mind's eye all in one glance. > > > > Now we can even extend that learning to asking a question of huge > > importance. Not with a truncated xaxis only but say a truncated x and > > y axis. Suppose we truncated the yaxis to be just 10 points in all > > and the xaxis its 2 points in all. Now the question of huge > > importance is "What are all the possible functions that exist in that > > truncated coordinate system?" > > > > Now in Old Math if ever such a question was asked > > "how many functions can exist (continuous functions)" the math > > professor would answer infinity number. In New Math, that question > > has a more precise answer. Of course it is a number larger than Floor > > pi*10^603, but in New Math, we can compute precisely what the total > > possible functions that can exist. > > > > For example, if we truncated the axes to just 2 points, 0 and > > 1*10^603 then the total number of functions that exists is 4 from > > probability theory. > > > > f1 = (0,0), (1*10^603,0) > > f2 = (0,0), (1*10^603,1*10^603) > > f3 = (0,1*10^603), (1*10^603,0) > > f4 = (0,1*10^603), (1*10^603,1*10^603) > > > > So, what is the huge number by probability theory for a nontruncated > > 1st quadrant of total possible functions of mathematics? > > > >  > > More than 90 percent of AP's posts are missing in the Google > > newsgroups author search archive from May 2012 to May 2013. Drexel > > University's Math Forum has done a far better job and many of those > > missing Google posts can be seen here: > > > > http://mathforum.org/kb/profile.jspa?userID=499986 > > > > Archimedes Plutonium > > http://www.iw.net/~a_plutonium > > whole entire Universe is just one big atom > > where dots of the electrondotcloud are galaxies
Any clear demonstration of your claims? All I see are simple examples. No theory. Only empty words.
Theorems and proofs please. Otherwise, you're meaningless... Examples are not theory.



