Date: May 21, 2013 4:55 PM Author: Inverse 18 Mathematics Subject: Re: Fundamental Theorem of Calculus is superfluous in New Math #9<br> TRUE CALCULUS; without the phony limit concept (textbook 1st ed.) On May 21,2013, Archimedes Plutonium wrote:

> Alright, I have come to some decisions at this stage of this tiny

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> textbook, that I shall make it no longer than 10 pages. I decided on

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> that because a bright Middle School student can handle 10 pages of

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> mathematics that he or she has never seen before and learn something.

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> However if 25 pages, they would likely be too discouraged. And also,

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> because True Calculus has no limit concept, that most of modern day

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> calculus of those 700 page texts, much of that gobbleygook phony

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> baloney or gibberish nattering nutter speak is about the limit. When

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> you have true math, you need just 10 pages to explain it. When you

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> have fake math, you need 700 pages of symbolism and abstractions to

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> hide and cover up.

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>

>

> So I have two pages remaining in this edition. And when I do the 2nd

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> edition I can do it all in two days posting 5 posts per day. So a

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> rapid fire book is this, because I can have the 100th edition within

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> one year.

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>

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> Now since this text is only 10 pages long, I need no chapters to

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> organize because from start to finish, anyone can read it in one day

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> and no point in dividing 10 pages into chapters.

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>

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> Now let me outline the education system of how calculus is taught in

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> Old Math. The first Calculus in the school system is called

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> "Precalculus" and it teaches about function, about area under graph

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> and about slope and tangents, but stops short of the limit concept.

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> Calculus taught in College is basically a year study of the "limit

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> concept". So in Old Math, calculus and limit concept were one and the

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> same.

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>

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> In New Math, we start first with the concept of finite moving into

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> infinity and have to find a borderline of where is the last finite

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> number and the start of infinity. I found that borderline to be Floor-

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> pi*10^603 where pi has three zero digits in a row and is evenly

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> divisible by 2,3,4,5 or 120. This divisibility is important for it

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> gives us the Euler regular polyhedra formula and it gives us where the

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> surface area of the pseudosphere equals the area of the corresponding

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> sphere. The inverse of that infinity borderline I denote as 1*10^-603

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> is the smallest nonzero number possible in mathematics and geometry.

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> It is the metric size of the hole or gap or empty space between 0 and

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> the next number which is 1*10^-603 and the next number after that is

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> 2*10^-603 and there are no numbers in between those three numbers

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> listed. There is just empty space, however one can draw a line or line

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> segment in that empty space even though there are no number points.

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>

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> So these holes and gaps make the limit concept as fictional, for there

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> is no need of a limit. The holes themselves serve as a limit. The

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> holes prevent pathological functions from forming such as the

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> Weierstrass function or the function y = sin(1/x).

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>

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> The holes allow the derivative to form or come into existence because

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> the hole gives the derivative room to form a angle, an angle between 0

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> and 90 degrees. Without the hole or empty space, the neighboring

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> infinite points would obstruct as in the Weierstrass function,

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> obstruct the formation of the derivative. But since every point in the

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> Cartesian Coordinate System is surrounded by a hole of at least

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> 10^-603, that every point of the function is differentiable.

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>

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> The holes allow the integral to come into existence because with the

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> empty space the integral is a summation of very thin picketfence

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> rectangles with a triangle on top of the rectangle. The hypotenuse of

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> the triangle top is the derivative. The integral is the summation of

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> all these picketfences whose width is exactly 10^-603. In Old Math,

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> the integral was a summation of line segments, but even Middle School

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> children have learned that lines and line segments have no area, yet

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> calculus professors seem to have lost sight of the fact that line

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> segments have no area when they explain calculus. So the hole of

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> 10^-603 allows the integral to form and exist.

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>

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> Now in most Old Math calculus texts of those 700 page gibbering

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> nattering nutter symbolism of limits, once they cover derivative and

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> integral, they usually want to tie the two together in what is called

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> the "Fundamental Theorem of Calculus". And they make a big stir and

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> fuss about this. But in New Math, we not only throw out the limit as

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> fakery, but we have no need to show that the derivative is the inverse

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> of integral and vice versa. In mathematics, do we need to have a

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> Fundamental theorem of add subtract or a Fundamental theorem of

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> multiply divide and prove they are inverses? No, we need not go

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> through that silliness.

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>

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> In New Math, in True Calculus we merely note that the derivative is

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> the angle of the hypotenuse atop the picketfence which determines a

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> unique area of the picketfence, so that the derivative is the inverse

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> of the integral. If I change the area of the picketfence, I change the

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> derivative proportional to the area. If I change the angle of the

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> hypotenuse, I proportionally change the area inside the picketfence.

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>

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> So in True Calculus we throw out the phony baloney limit concept and

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> along with it we have no need for a hyped up exaggerated Fundamental

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> theorem.

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>

> Now let me speak more about geometry, since I have just these 2 last

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> pages. It is important to know the relationship of geometry to numbers

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> and that should have been the Fundamental Theorem of Calculus. The

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> fundamental theorem should have embodied the idea that why the

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> Calculus exists at all is because in Euclidean Geometry when we have a

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> Cartesian Coordinate System of dots separated by 10^-603 holes, that

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> no matter what the size of the graph is, the relationships of where

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> those dots are to each other always forms the same angles. So that the

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> function y= x is always a 45 degree angle. So the Fundamental Theorem

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> of Calculus should have been a theorem that explores and proves why

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> Euclidean Geometry can yield a calculus but that Elliptic geometry or

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> Hyperbolic geometry cannot yield a calculus.

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>

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> And another geometry feature I want to start to explore is a truncated

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> Cartesian Coordinate System.

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> Here I have just two points for the x-axis of 0 and 1*10^-603 and I

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> have all the points of the y-axis from 0 to 10^603 or 10^1206 points

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> in all. Now I call that a truncated Coordinate System of the 1st

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> quadrant. And you maybe surprized as to how much one can learn from

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> this truncated system. It has the functions of y=3, and y=x, and

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> y=x^2. It also has the functions of Weierstrass function and the

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> function y = sin(1/x).

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>

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> So for the function y=3 we plot the point (0,3) and (1*10^-603, 3). It

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> has the function y=x and we plot the point (0,0) and (1*10^-603,

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> 1*10^-603).

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>

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> What is nice about the truncated-Coordinate System is that we can

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> instantly learn a lot about functions without being bogged down with

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> distractions of a lot of point plotting. We can home in on just the

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> derivative or integral in that truncated interval and we can see how

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> in New Math, all the points and numbers of mathematics should be

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> transparent and visible to the mind's eye all in one glance.

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>

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> Now we can even extend that learning to asking a question of huge

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> importance. Not with a truncated x-axis only but say a truncated x and

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> y axis. Suppose we truncated the y-axis to be just 10 points in all

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> and the x-axis its 2 points in all. Now the question of huge

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> importance is "What are all the possible functions that exist in that

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> truncated coordinate system?"

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> Now in Old Math if ever such a question was asked

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> "how many functions can exist (continuous functions)" the math

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> professor would answer-- infinity number. In New Math, that question

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> has a more precise answer. Of course it is a number larger than Floor-

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> pi*10^603, but in New Math, we can compute precisely what the total

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> possible functions that can exist.

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> For example, if we truncated the axes to just 2 points, 0 and

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> 1*10^-603 then the total number of functions that exists is 4 from

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> probability theory.

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> f1 = (0,0), (1*10^-603,0)

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> f2 = (0,0), (1*10^-603,1*10^-603)

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> f3 = (0,1*10^-603), (1*10^-603,0)

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> f4 = (0,1*10^-603), (1*10^-603,1*10^-603)

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> So, what is the huge number by probability theory for a nontruncated

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> 1st quadrant of total possible functions of mathematics?

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>

>

> --

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> More than 90 percent of AP's posts are missing in the Google

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> newsgroups author search archive from May 2012 to May 2013. Drexel

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> University's Math Forum has done a far better job and many of those

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> missing Google posts can be seen here:

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>

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> http://mathforum.org/kb/profile.jspa?userID=499986

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>

>

> Archimedes Plutonium

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> http://www.iw.net/~a_plutonium

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> whole entire Universe is just one big atom

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> 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.