The Inquisition and Reformation on Fundamental Mathematics Concept

• 1、Department of Mathematics,Henan Polytechnic University,jiaozuo 454000

Abstract：The formalist logic could not make mathematics system possessed consistency. Materialist dialectics is necessary method to explain mathematics concept. The fundamental terminologies in mathematics are all almost the ideal object. Ideal objects are all depended on the existence. Infinite set is the limit of infinite sequence of finite set, and the limit possesses the nature of it could not be reached. The true sense of infinite decimal, infinity, and infinitesimal are all the infinite sequence. The true value of length of line segment is the limit of approximate value sequence, where error bounds tend to 0. The ideal real number is the limit of rational number sequence; the ideal point is the limit of approximate point sequence; the ideal parallel line is the limit of approximate parallel line sequence; and the above limits possess all the nature of it could not be reached. The true sense of twinkling velocity is sufficiently exactly approximate value of average value on sufficiently small time segment. The approximation method satisfied error bounds condition and the method approached step by step are fundamental method to settle continuous real quantity.

Keywords： Infinity Infinite set Point Real number Parallel line Mathematical induction excluded middle The infinity nature to cut segment of time and line