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Topic: Fundamental Theorem of Calculus is superfluous in New Math #9 TRUE
CALCULUS; without the phony limit concept (textbook 1st ed.)

Replies: 3   Last Post: May 22, 2013 1:20 AM

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Inverse 18 Mathematics

Posts: 175
Registered: 7/23/10
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
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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 x-axis of 0 and 1*10^-603 and I
>
> have all the points of the y-axis 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 truncated-Coordinate 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 x-axis only but say a truncated x and
>
> y axis. Suppose we truncated the y-axis to be just 10 points in all
>
> and the x-axis 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 electron-dot-cloud 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.



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