与“无穷”相关的数学基础的革命:“新无穷观—新数量体系—新极限论”与“无穷悖论综合征”的解决

A Revolution in the “Infinite” Related Foundation of Mathematics: “New infinite notion-new infinite number system-new limit theory”and Solving “Infinite Paradox Syndrome”

从"概念、数量观、形式语言"三个角度认识新、旧无穷体系之间的主要区别,研究芝诺悖论、贝克莱悖论和罗素悖论"三胞胎"千百年来悬而未决且不断繁衍壮大的原因及由它们所揭示的现有传统无穷体系基础中的缺陷.得到两个明确的结论,(1)现有传统无穷体系基础的缺陷决定了这三个悖论之间实际上是"三胞胎"关系,应该整合它们所揭示的问题,进行系统性研究;(2)自古以来在这个领域中那种错误的"忽视基础理论研究"的工作思路使人们无法认识这三个悖论的本质、无法解决它们所揭示的问题,以"新无穷观—新数量体系—新极限论"为基础的新无穷体系的产生是与"无穷"相关的数学基础的革命.

From three angles of“concept, number notion, formal language”, the fundamental differences in classi-cal and newly constructed infinite theory systems are studied and the reasons of why the family members of Zeno-Berkeley-Russell’s Paradoxes have been keeping increasing are investigated.Two conclusions are drown：（1）The three paradoxes are actually“Triplets”produced by the same defects in present classical infinite theory system, we should integrate the defects and engage a systematic research; （2）The mistaken working idea of“ne-glecting the fundamental research”in this field since antiquity has been unable people to understand the natures of these three paradoxes and to solve the defects disclosed by them, the birth of new infinite theory system basing on“new infinite notion-new infinite number system-new limit theory”is a revolution in the infinite related foundation of mathematics.