```Date: May 25, 2013 1:43 AM
Author: plutonium.archimedes@gmail.com
Subject: Maxwell Equations as axioms over all of physics and math #9 Textbook<br> 2nd ed. :  TRUE CALCULUS; without the phony limit concept

Alright, I am learning more new things, for in this 2nd edition I havean alternative to the picketfence model. I have the pure and straightrectangle model and the pure and straight triangle. In the rectanglemodel we fill the dx of 10^-603 width and the height is y itself. Inthe pure triangle we have a right triangle on the leftside of thepoint of the graph and the same triangle on the rightside with itshypotenuse in the reverse direction as pictured like this:     /|  /   |/ __|unioned with this triangle|\|  \|__\is the same area as the rectangle model of the point on the functiongraph.The problem, though, is that the angle of the hypotenuse does not likelike the slope or tangent to the point of that function graph. So Ineed to see if that hypotenuse is related to the slope or tangent orderivative at that specific point. If it is, then, clearly we see howderivative is the inverse of integral, because both have the same areaand the triangle hypotenuse would be the derivative. So instead ofrectangles forming the integral we can take two triangles. Sohopefully I can work this out in the 3rd edition which I plan to startin the next day or so.Alright, this is the 10th page of the 2nd edition and the last page. Iwant to devote the last page to showing how all this math is begotfrom the Maxwell Equations.Now on this last page I want to show how Calculus of its empty spacebetween successive numbers is derived from the Maxwell Equations asthe ultimate axiom set over all of mathematics. The Maxwell Equationsderives the Peano axioms and the Hilbert axioms. But I want to showthat the Maxwell Equations do not allow for the Reals to be acontinuum of points in geometry but rather, much like the integers,where there is a empty space between successive integers.The Reals that compose the x-axis of 1st quadrant are these:0,  1*10^-603,  2*10^-603,  3*10^-603, 4*10^-603, 5*10^-603,6*10^-603 . . on up to 10^603Pictorially the Reals of the x-axis looks like this...................>and not like this____________>So in the Maxwell Equations we simply have to ask, is there anythingin physics that is a continuum or is everything atomized with emptyspace in between? Is everything quantized with empty space inbetween?I believe the answer lies with the Gauss law of electricity, commonlyknown as the Coulomb law. The negative electric charge attracts thepositive electric charge, yet with all that attraction they still mustbe separated by empty space. If there was a continuum of matter inphysics, then the electron would be stuck to the proton. The verymeaning of quantum mechanics is discreteness, not a continuum.Discreteness means having holes or empty space between two particlesinteracting of the Maxwell Equations.So if physics has no material continuum, why should a minor subset ofphysics-- mathematics have continuums. If Physics does not havesomething, then mathematics surely does not have it.Now I end with reminders for the 3rd edition:       REMINDERS:(1) First page talk about why Calculus exists as an operator  ofderivative versus integral much the same way of add subtract or ofmultiply divide because in a Cartesian Coordinate System the number-points are so spaced and arranged in order that this spatialarrangement yields an angle that is fixed. So that if you have anidentity function y = x, the position of points (1,1) from (2,2) isalways a 45 degree angle. So Calculus of derivative and integral isbased on this fact of Euclidean Geometry that the coordinates are sospatially arranged as to yield a fixed angle. Numbers forming fixedangles gives us Calculus.(2) Somewhere I should find out if the picketfence model is the verybest, for it maybe the case that a rectangle model versus a puretriangle model may be better use of the empty space of 10^-603 betweensuccessive Reals (number points). The picketfence model is good, butit never dawned on me until now that there is likely a better modeleven yet-- pure rectangle versus two pure triangles. My glitch is toget the hypotenuse related to the derivative. If I can solve thatglitch, I have a crystal clear understanding of the derivative,integral and why they are inverses.(3) I am really excited about that new method of arriving at theinfinity borderline of Floor-pi*10^603 via Calculus. The first numberwhich allows a half circle function to be replaced by a 10^1206derivatives of tiny straight line segments and still be a truncatedregular polyhedra, is when pi has those 603 digits rightward of thedecimal point. The derivative of half circles of any number smallerthan Floor-pi*10^603 does not form a circle. And is that not whatCalculus is all about in the first place-- taking curves and findingEuclidean straight line segments as derivative and area. Calculus isthe interpretation of curved lines into straight line segments. So,onwards to 3rd edition.--More than 90 percent of AP's posts are missing in the Googlenewsgroups author search archive from May 2012 to May 2013. DrexelUniversity's Math Forum has done a far better job and many of thosemissing Google posts can be seen here:http://mathforum.org/kb/profile.jspa?userID=499986Archimedes Plutoniumhttp://www.iw.net/~a_plutoniumwhole entire Universe is just one big atomwhere dots of the electron-dot-cloud are galaxies
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