论“无穷事物”的定量认知(Ⅸ)--新开发的“无穷载体理论”中“无穷载体基因”与“无穷载体尺度”  

On the Quantitative Cognitions to “Infinite Things”(Ⅸ)--“The Infinite Carrier Gene” and “ The Infinite Carrier Measure” in the Newly Developed “Infinite Carrier Theory”

作　　者：欧阳耿[1] OUYANG Geng(Department of Mathematics,Minnan Normal University,Zhangzhou 363000,Fujian,China)

机构地区：[1]闽南师范大学数学系,福建漳州363000

出　　处：《喀什大学学报》2020年第6期21-28,共8页Journal of Kashi University

摘　　要：以现有数学分析和集合论中三个著名的悖论为典型案例,从一个新的角度分析、揭示现有数学分析和集合论中无法避免的“定量认知基础理论缺陷”.结果表明,正是以无法科学定义、互相矛盾、空洞的“潜无穷—实无穷”概念为基础的现有经典无穷理论体系中整个“无穷载体理论”缺失,必然导致与“无穷”概念相关的现有数学领域中悬而未决的“无穷悖论症状群”的存在.基于“抽象概念的载体基因(无穷数学载体基因)”、“抽象概念的载体尺度(无穷数学载体尺度)”新概念,新开发的“无穷数学载体理论(迟到的‘实无穷理论’)”弥补了集合论、数学分析、一一对应理论和极限论的基础理论缺失,使人们有能力科学、有效、系统地开展对无穷数学事物的定量认知工作.Taking three outstanding paradoxes in the existing mathematical analysis and set theory as typical cases,the unavoidable defects of the basic theory of quantitative cognition in the existing mathematical analysis and set theory are analyzed and revealed from a new perspective.A clear conclusion has been reached:it is the lack of“infinite carrier theory”in the foundation of the existing classical infinite theory system basing on the contradictory,empty and non scientific defined“potential infinite-actual infinite”concepts that leads to the suspended“infinite paradox symptom clusters”in present infinite related fields of mathematics.In this paper,new concepts of“infinite carrier gene”and“infinite carrier measure(The Geng OUYANG Measure)”are given.The newly developed“Infinite Mathematical Carrier Theory(the late coming‘Actual Infinite Theory’)”makes up for the lack of basic theories of mathematical analysis,set theory,limit theory and one-to-one correspondence theory,so that people are able to carry out scientifically,effectively and systematically the work of quantitative cognitions to infinite mathematical things.

关 键 词：无穷悖论症状群 新无穷理论体系 无穷数学载体 无穷数学载体基因 无穷数学载体尺度 迟到的“实无穷理论” 

分 类 号：N02[自然科学总论—科学技术哲学] O143[理学—数学]