集合悖论再议

Reconsideration of Set Paradox

集合悖论的出现引发了世界数学界的震惊,史称第三次数学危机。针对集合论初创阶段逻辑结构还不够完善现象,数学家们尝试从逻辑上去寻找问题的症结,ZFC公理集合理论的提出,暂时避免了引发数学史上集合悖论的出现,但也不能说,危机就此完美解决。悖论破译的过程就是数学大发展之时,ZFC公理集合理论、模糊数学、集对分析等分支就是探索一种解决和处理集合的新方法。集对分析仍处于发展之中,若将经典微积分求系统变化率与集对分析理论求层次演化率相结合研究,定会促进集对分析向前发展。

The emergence of set paradox has shocked all of the mathematicians around the world.It is called the third mathematics crisis.In view of the lack of perfect logic structure in the initial stage of set theory,mathematicians try to find the crux of the problem from logic.The proposal of ZFC axiom set theory has temporarily avoided the emergence of set paradox in the history of mathematics,but it can not be said that the crisis has been solved perfectly.The process of paradox deciphering is the time when mathematics obtains big development.The ZFC axiom set theory,fuzzy mathematics,set pair analysis and other branches are the new solutions to solve and deal with the set problem.The set pair analysis is still in the process of development.If we combine the solution of system change rate in classical calculus with the solution of hierarchical evolution rate in set pair analysis,it will promote the development of set pair analysis.