how the limit concept destroys the derivative & integral #8 TRUE CALCULUS; without the phony limit concept (textbook 1st ed.)

[Archimedes Plutonium]

Alright, we covered derivative and integral. We understand that the
picketfence model is the essence of the derivative and integral, in
that a empty space is required between successive numbers. The metric
of that empty space is the inverse of the borderline of finite with
infinite. That metric is Floor-pi*10^603 with its inverse abbreviated
as 10^-603.

In Old Math, the limit concept destroys the integral because it
demands that the summation of rectangles has 0 width, in other words,
rectangles that are not rectangles but rather line segments. Now if
you believe a line segment or line can have area, well, then join the
millions of other fools who accept Old Math Calculus.

The limit concept destroys the derivative because it allows no room,
no empty space for the dy/dx to form an angle without the interference
of neighboring points of the function. When you have a empty space, a
hole or gap that is 10^-603 from neighboring points, that empty space
gives the function the freedom to form any angle between 0 degrees and
90 degrees (excluding 90 itself for then it is no longer a function).

So, a empty space between successive numbers is essential and required
for the Calculus to exist. The empty space gives the integral a
nonzero area for its picketfences that are summed over the graph of
the function, and the empty space gives the derivative room enough
that an angle is formed between a point and its neighboring points.

So that in Old Math with their phony limit concept, they coughed up
silly and fictional functions such as the Weierstrass function. They
did get something correct about the Weierstrass function for they call
it a pathological function as seen in the Wikipedia entry of this
function. In New Math with holes of 10^-603 there are no pathological
functions. In New Math, all continuous functions are differentiable
everywhere.

Now even Strang in his textbook CALCULUS, 1991 on page 86 shows us
what can be considered another pathological function when you have a
phony concept of limit. Strang shows us the function y= sin(1/x).
Strang thinks it is discontinous because it fluctuates so wildly when
it comes near 0. However, if Strang in his mathematics career had ever
considered that finite to infinity had a borderline and the inverse of
which imposes a hole or gap between successive numbers and that the
Calculus depended on that hole and gap so that the x-axis of
mathematics does not look like this:

______________>

but rather, the x-axis of true mathematics looks like this:

...................................>

and that all lines and line segments have a 10^-603 hole or gap of
empty space between successive numbers.

So that if Weierstrass or Strang had done a Cartesian Coordinate
System Grid of the x-axis and y-axis in the First Quadrant of those
dots with 10^-603 holes, that the Weierstrass function and the
function y= sin(1/x) are simply normal functions as normal and easy as
y= x.

Now let me spend a few minutes here on doing what Weierstrass or
Strang would call a pathological function or a oscillating wild
function that was discontinuous, when in truth, it is a normal
function.

So we have the entire grid system of the 1st quadrant:

...
...
...

Now I showed only 3 numbers of x-axis and 3 numbers of y-axis but for
the full grid in 1st quadrant I would need 10^1206 dots for x and y
axis. And the total dots would be 10^2412. Now for the function that
alternates between y value of 0 and y value of 10^603. So, when x=0
then y=0, now the next number is 1*10^-603 and when x is that number
then y is the number 10^603, and the next number is x= 2*10^-603 and
y value is 0, and this alternates on and on, as a huge saw-blade
pattern. It reminds us of the Weierstrass function shown in Wikipedia
and reminds us of the Strang function y= sin(1/x) near 0.

Now in New Math, this saw-blade pattern has the steepest angle
possible of the 1st quadrant yet not 90 degrees itself but close to 90
degrees. It is continuous everywhere for continuity is defined as
having a picketfence width no greater than 10^-603. It is
differentiable everywhere for every point of the function graph has a
10^-603 empty space to allow the derivative angle freedom to be any
angle from 0 to 90 degrees (except 90 itself). And it is integrable
everywhere because each picketfence has a valid area.

In Old Math, with their limit concept, since infinity is never
properly defined by a borderline, a pathological function is easily
borne in that mess, because any pattern can be made into a fractal
that as the limit gets smaller and smaller, the pattern just gets
smaller and smaller following the limit and suffocating the limit so
that no derivative can be obtained. Whereas in New Math, once you
reach 10^-603, your wild oscillations of Strang or your fractal
pattern of Weierstrass cease or stop at 10^-603.

So let me summarize at this juncture of True Calculus. When
mathematics properly defines the borderline between finite and
infinite, it produces a large number, such as where pi digits have
their first three zero digits in a row, and the inverse of this
borderline is the smallest nonzero number or point of geometry. That
forces the Cartesian Coordinate System to have empty space holes or
gaps between successive numbers. The holes or gaps allow a derivative
to freely have a angle and thus the derivative can be formed. The
holes also give area for the smallest rectangles or picketfences and
thus allows the integral to be formed.

--

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