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Topic: Axiom mistakes of Euclidean Plane Geometry #1 Uni-textbook 6th ed.:
TRUE CALCULUS; without the phony limit concept

Replies: 10   Last Post: Jun 23, 2013 3:30 PM

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 plutonium.archimedes@gmail.com Posts: 14,663 Registered: 3/31/08
Axiom mistakes of Euclidean Plane Geometry #1 Uni-textbook 6th ed.:
TRUE CALCULUS; without the phony limit concept

Posted: Jun 19, 2013 2:01 PM

Alright I am happy with the High School textbook of 10 pages long and
now will write the University or College textbook. I want both texts
consolidated into one book. The Uni text should be 40 pages or less,
so the entire text is 50 pages or less.

Too many errors and mistakes are taught both to the High School and
University students. The three largest and gravest errors are these
three:

1) no borderline between finite and infinity, thus prompting shoddy
mathematicians to impose a limit concept, a utterly fake and phony
concept which may allow these shoddy mathematicians to talk about
Calculus, even though they fail to know and understand true calculus

2) never a correction of the mistakes of the axioms of Euclidean
geometry and its modern day revision as that of the Hilbert axioms

3) failure to realize the derivative must be a part of the actual
function graph and not a separate independent entity

This college and university text of True Calculus addresses those
major mistakes and flaws of Calculus and teaches the student what
Calculus truly is. This book is the very best book written on Calculus
since Leibniz and Newton discovered the Calculus circa 1684 (Nova
methodus) and 1671 (Methodus Fluxionum) respectively.

I start this Uni text where I left off with the HS (High School) text,
talking about the errors and mistakes of the Euclidean Plane Geometry
axioms.

Let us focus on two axioms of Euclidean Plane Geometry and as stated
in Hilbert's vast revision of those axioms.

Points of geometry

Lines and line segments of geometry

In the Hilbert axioms of geometry, and all other axiom sets, they had
that a point has no length, no width, no depth, yet they also had that
a line or line segment has no width, no depth, but does have length.

Neither Hilbert nor all the mathematicians after Hilbert, realized
that their axioms of line and line segment and point were
contradictory, for you cannot have a line with length composed of
points with no length. To escape that logical contradiction, you must
impose the idea that length comes about by the concept of empty space
between points, so that a line is composed of not just points but of
points with empty space between successive points.

So to correct Hilbert we have this:

point axiom: a point has no length, no width, no depth

line axiom: a line or line segment is composed of successive points
with empty space between the points and the line has no width, no
depth, but has length due to the summation of the empty spaces.

Now the sloppy and shoddy mathematicians reconciled the line having
length by considering the idea of the enormous density of points that
compose a line or line segment. Their flawed reasoning was that if the
density of points with no length, no width, no depth if that enormous
density went into composing a line or line segment that it would have
length due to that density. But then, if you make a silly arguement of
density for length, then there is no stopping you from saying the line
or line segment has width and depth due to density of points.

So, in one fell swoop, we find the Euclidean Plane Geometry axioms
with its Hilbert revision as totally flawed and need of major repair.
We find the repair to be that the axioms of geometry need to have
points as successive points with empty space in between successive
points. Much like the Integers of mathematics are successive points as
that of 1 then 2 then 3 then 4 then 5, etc. So between 1 and 2 is
empty space and a line that is 5 units long, has length, not because
it has number points of 0,1,2,3,4,5, but because it has those empty
spaces between 0 and 1 then 1 and 2, etc. In this text of True
Calculus, the integers are too large of empty space, so in this text
we find that successive number points of 1*10^-603 fits perfectly for
mathematics.

So we start this Calculus text for college and university students,
True Calculus by correcting a major error and flaw of Old Math of
their Euclidean Geometry axioms. It is a major flaw for it prevents us
from achieving or attaining True Calculus, and is such a sad flaw that
it encourages the retention of the phony and fake limit concept. When
you have Fake Calculus, you need textbooks that are hundreds of pages
long, for most college texts on Calculus such as Strang, Stewart,
Fisher & Ziebur, Ellis & Gulick are approaching or exceeding 700
pages, because they have to devote most of their time on the phony
limit concept. When you have True Calculus, it can be explained and
done with in 10 pages. Fake Calculus takes about 700 pages, and True
Calculus takes but 10 pages.

--

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

Thanks to Google for returning the option of crossposting, for
yesterday, 18 June 2013 Google allowed only singular newsgroups and no
crossposting.

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