Abstract In accordance with formalism, one of the two most widely accepted foundations for modern mathematics, an experimental axiomatic system having a variant number theory is admissible for study if it is self-consistent.  Nonetheless, any given "revised" system is without exceptional theoretical value or applicability unless it is comparatively advantageous to the "conventional" system. This unconventional work initially involves the creation of a revised multiplication in which the revised product of two negative factors equals a negative real number, contrary to conventional multiplication.  This precludes the existence of the unit imaginary number and thus, the complex number system. By a method analogous to how conventional involution is built upon conventional multiplication, likewise is revised involution built upon revised multiplication.  Although addition is identical under both systems, with two of the three binary operations revised, a revised arithmetic exists and consequently, a revised algebra.  Further ramifications include a revised analytic geometry and revised calculus.  In fact, every branch of mathematics which is wholly or partially based upon numerical definitions is affected. Comparatively, revised arithmetic requires three number systems instead of seven (i.e., no complex or hypercomplex number systems: quaternion, octonion, sedenion) and three binary operations instead of six (i.e., no inverse binary operations: subtraction, division, evolution) yet maintains all comparable problem-solving capabilities. In revised algebra, a binomial, linear equation to the nth (any) degree is solvable since after revised cross-multiplication, it is reducible to the original, first degree equation.  In conventional algebra, a binomial, linear equation to the fifth degree or higher is generally impossible to derive solutions for.  Through it all, any valid algebraic equation which is solvable by the conventional complex number system is likewise solvable by the revised real number system. Ultimately, the two numerical systems are fully isomorphic in describing the same underlying mathematical reality as it exists independent of any contrasting, arbitrarily-invented, mathematical languages of interpretation.

"Symmetry establishes a ridiculous and wonderful cousinship between objects, phenomena and theories outwardly unrelated:  terrestrial magnetism, women's veils, polarized light, natural selection, the theory of groups, structure of space, vase designs, quantum physics, scarabs, flower petals, X-ray interference patterns, cell division in sea urchins, equilibrium positions of crystals, Romanesque cathedrals, snowflakes, music, the theory of relativity ..." - Hermann Weyl   mathematical physicist

Download "symmetry.exe" (1130 KB), a safe self-extracting compressed file, which contains the entire project featuring 2 files:     Entire text including 11 quality, color graphs ("paper.pdf")-         338 pages.  [Requires Adobe Acrobat Reader.] Adobe Acrobat Reader Free Download www.adobe.com/products/acrobat/readstep2.html     Demo program for revised arithmetic ("math.exe").         [Installs and runs under any MS Windows operating system.] latest revision May 26, 2007 If you prefer NOT to have to download such a large file, I am willing to mail the entire project to you on 1 DVD or CD (free, to anywhere in the world).  I respond to requests quickly and reliably.

Graph Viewing Cabinet     Adobe Acrobat Reader plug-in is required.  Display quality directly thru the plug-in is marginal.  It is better if viewed after download via Adobe Acrobat Reader.  Note-  Do not expect to totally understand the graphs unless-until you have already read the entire paper. Containing 11 quality, color graphs of functions, models, binary operations:     Opposition Reciprocation Opposition & Reciprocation Extended Real Number Continuum Addition Revised Multiplication Revised Involution Revised Slope System Revised Power Functions Revised Exponential/Logarithmic Functions  (x y± axes) Revised Exponential/Logarithmic Functions  (x± y axes)

ISIS- Symmetry                 www.mi.sanu.ac.yu/~jablans/isis0.htm                    A Timeline Of Symmetry                 www.theophys.kth.se/mathphys/SYM/sym_history.html                    Number Theory Web                 www.dpmms.cam.ac.uk/Number-Theory-Web                    Diophantine & Non-Diophantine Arithmetics                 Dr. Mark Burgin                 http://arxiv.org/ftp/math/papers/0108/0108149.pdf                    The Math Forum                 Drexel University                  http://mathforum.org/library/view/61309.html                    Reviews of Mathematical Works                 Miguel Iradier                  www.hurqualya.com/proyect.htm                    The MASM Forum                 symmetrical math calculator                  An Extremely Long Link- Just Click Here!