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20120524-Lev_Gelimson-Unimathematics-Mega-Overmathematics-Revolutions-Megasystem-Munich-Russian.avi

The "Collegium" All World Academy of Sciences Academic Institute for Creating Universal Sciences (Munich, Germany) Ph. D. & Dr. Sc. Lev Gelimson's Own Uni(Mega-Over)mathematics & Uniphysics (Unimetrology, Unimechanics, & Unistrength): Universal Fundamental Sciences Systems, Revolutions, Inventions, Discovering New Phenomena and First Strength Laws of Nature VIP in the Encyclopedia "Who is Who" http://kekmir.ru/members/person_6149.... http://fusc.is-great.org http://scie.is-great.org http://fusc.lima-city.de http://scie.freehostia.com http://scie.de.vu Mega-Overmathematics as a Megasystem of Revolutions in Mathematics May 24, 2012. Munich Mega-overmathematics is a system of many diverse overmathematics which differ by possible hyper-Archimedean structure-preserving extensions of the real numbers via including both specific subsets of some infinite cardinal numbers as canonic positive infinities and signed zeroes reciprocals as canonic overinfinities, which gives the uninumbers. They provide adequately considering, setting, and very efficiently quantitatively solving many typical urgent problems. In the introduced uniarithmetics, quantialgebra, and quantianalysis of the finite, the infinite, and the overinfinite with quantioperations and quantirelations, the uninumbers evaluate and are interpreted by quantisets algebraically quantioperable with any quantity of each element and with universal, perfectly sensitive, and even uncountably algebraically additive uniquantities so that universal conservation laws hold. Quantification builds quantielements, integer and fractional quantisets, mereologic quantiaggregates (quanticontents), and quantisystems with unifying mereology and set theory. Negativity conserving multiplication, base sign conserving exponentiation, exponentiation hyperefficiency, composite (combined) commutative overoperations, quanti-hyperroot logarithms, self-hyperroot logarithms, the voiding (emptifying) neutral element (operand), and operations with noninteger and uncountable quantities of operands are also introduced. Division by zero is regarded when necessary and useful only and is efficiently utilized to create overinfinities. Positional quantisets, quantimappings, quantisuccessions, successible quantisets, quantiorders, orderable quantisets, quantistructures, quanticorrespondences, and quantirelation systems are also introduced. The same holds for quantitimes, potential quanti-infinities, general infinities, subcritical, critical, and supercritical quantistates and quantistate processes, as well as quasicritical quantirelations. Quantidestructurizators, quantidiscriminators, quanticontrollers, quantimeaners, quantimean systems, quantibounders, quantibound systems, quantitruncators, quantilevelers, quantilevel systems, quantilimiters, quantiseries estimators, quantimeasurers, quantimeasure systems, quanti-integrators, quanti-integral systems, quantiprobabilers, quantiprobability systems, and central estimators efficiently provide quantimeasuring and quantiestimating. The unierror corrects and generalizes the relative error. The reserve, reliability, and risk based on the unierror additionally estimate and discriminate exact objects, models, and solutions by the confidence in their exactness with avoiding unnecessary randomization. All these estimators first evaluate both the inconsistency of a general problem as a quantisystem which includes unknown quantisubsystems and its pseudosolutions including quasisolutions and antisolutions. Multiple-sources iteration and especially intelligent iteration are much more efficient than single-source iteration. Sufficiently increasing the exponent by power mean methods and theories can bring adequate results. This holds for linear and nonlinear bisector methods and theories with distance or unierror minimization, reserve maximization, as well as for distance, unierror, and reserve equalization. Uniquantitative data coordinate and/or bisector partitioning, grouping, bounding, leveling, scatter and trend measurement and estimation very efficiently provide adequate data processing with efficient utilization of outliers and possibly recovering true measurement information using incomplete changed data. Infinite, overinfinite, infinitesimal, and overinfinitesimal continualization provides perfect computer modeling of any uninumbers. Perfectioning built-in standard functions brings proper computing. Universal algorithms ensure avoiding computer zeroes and infinities with computer intelligence and universal cryptography systems hierarchies. It becomes possible to adequately consider, model, express, measure, evaluate, estimate, overcome, and even efficiently utilize many complications such as contradictions, infringements, damages, hindrances, obstacles, restrictions, mistakes, distortions, errors, information incompleteness, variability, etc. Mega-overmathematics also includes knowledge uniquantitative test and development fundamental metasciences