Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.


Math Forum
»
Discussions
»
sci.math.*
»
sci.math
Topic:
Axiom mistakes of Euclidean Plane Geometry #1 Unitextbook 6th ed.: TRUE CALCULUS; without the phony limit concept
Replies:
10
Last Post:
Jun 23, 2013 3:30 PM




Axiom mistakes of Euclidean Plane Geometry #1 Unitextbook 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 electrondotcloud are galaxies



