数学理论体系改革的绪论

In the process of studying mathematical theory, there have been paradoxes, crises and contradictions for thousands of years. The purpose of establishing mathematical theory is to solve practical problems in production. Complete and non-contradictory pure mathematical theory can not be established. Therefore, materialist dialectics should be taken as the fundamental method to establish mathematical theory. And put forward that the essence oIntroduction to the Reform of Mathematica Theory Systemf mathematics is the science of describing the size, and relationship of the real quantity; the size and quantity of the real quantity has variability, as long as it is described enough to meet the actual needs of production. Mathematical theory needs to be perfected and matured gradually in the application process of continuing practice, The compatibility of mathematical theory depends on the compatibility of the real world. The establishment of mathematical theory is inseparable from the knowledge of language and philosophy, and can not be separated from practice. The infinite meaning is that there is no exhaustion and no end. The infinite quantity in mathematical analysis is a variable. Its generalized limit is an abnormal number +∞ (called by ideal infinity or Endless evil), The infinite decimal is the abbreviation of the convergence sequence of the lower decimal approximate value of the ideal real number. Ideal sum, approximate sum and omnipotent approximate sum are needed for infinite series. Differentiation of self-variable is a sufficiently small dialectical number whose limit is 0+. The unity of opposites between ideal and reality, infinite also and finite, precise and approximate interdependence and mutual struggle are the fundamental principles of expounding mathematical theory. Practice is the ultimate and sole criterion for testing truth.