delta concept of limit #5 TRUE CALCULUS; without the phony limit concept (textbook 1st ed.)

[Archimedes Plutonium]

Alright I can make this textbook 25 pages or less. And let me put the
chapters and subject into the title of the post. I am just about to
start the chapter on integrals and integration but I must return to #3
posting-page and make a error correction change. It is not so much an
error on my part as a obfuscation on my part. The troubling idea is
this interval which is lopsided should be an equal delta on both sides
of the point, and thus obfuscates why the limit is phony. So let me
correct that obfuscation.

On May 20, 1:13 am, Archimedes Plutonium
<plutonium.archime...@gmail.com> wrote:

(snipped)

Now here is the start of the obfuscation

>
> Now let us review the function y = x^2 with its derivative of y' = 2x
> so that for the point x=3, then y was 9, and the slope or tangent at
> x= 3 was 6.
> And we looked at the point to the left of 3 which is 2 and the point
> to the right of 3 which is 4 to see that the change in y was 16-4
> while the change in x was 4-2 which we have dy/dx as 12/2 = 6. But
> what if we made the interval further apart from 3. What if we made the
> interval from x=2 to x=5 then our dy/dx is
> (25-4)/(5-2) would be 21/3 is 7, and 7 is not the exact derivative of
> 6.

I made an example with a lopsided delta of the limit concept for there
is only 1 unit to the left of 3 while there are 2 units to the
rightwards of 3. So that if I had the limit delta to be 1 to 5 with 3
in the middle, I end up with (25-1)/(4-1) = 6

So now, let me give an example of a delta limit concept that does fall
apart for the function of y=x^2 with its derivative y'= 2x.

So let me replace that example with x=pi and 1 unit distance on both
sides of pi as the delta of the limit concept.

So I have my point as pi and the delta interval is pi+1
and pi-1. And here I go through the same procedure as Old Math, where
the derivative at point pi for function y=x^2 is 2x and the derivative
at x=pi is thus 2pi. However, I want to actually do the dy/dx. So here
I have (2.14159..)^2 and (4.14159..)^2. The dx term is simple enough
as the interval measures 2 units. However, the delta limit concept
falls apart for the dy term and does not yield the exact 2pi.

Now I could use the number "e" rather than pi and achieve the same
failure.

However, in New Math, there is never a failure of obtaining the exact
derivative because every number point in the graph is separated by a
10^-603 hole or gap on both sides of the number point, so that the dy
and dx of dy/dx are exact. You see, when you demark the border between
finite and infinite, you demark the hole or gap between neighboring
number points and that hole or gap makes the limit delta concept
superfluous.

So for pi we have Floor-pi*10^603 which means we have pi to the digits
of 603 digits rightward of the decimal point and the last three digits
end in three zeroes in a row.
Now because of those 603 digits and because the holes in the Cartesian
Coordinate System Grid are holes the inverse of Floor-pi*10^603, that
the dy/dx matches exactly the derivative 2pi.

Now there are many other examples of where the dy/dx do not match
exactly the derivative value, but the functions are more complicated
than my three simple functions of this textbook.


--

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