论“无穷事物”的定量认知(Ⅷ)——新、旧无穷集合论和数学分析基础理论中的三个不同特征  

On the Quantitative Cognitions to“Infinite Things”(Ⅷ)——Three Different Fundamental Characteristics in the Old and New Generations of Infinite Set Theory and Mathematical Analysis

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3期27-33,共7页Journal of Kashi University

摘　　要：从最原始的基础入手,研究证明了无法科学定义、互相矛盾的“潜无穷—实无穷”概念是现有经典无穷理论体系的基础,以经典无穷理论体系为基础的现有经典数学分析和集合论自古以来都存在完全相同的三个基础理论缺陷,人们只能在缺乏科学基础理论的状态下摸索前进.虽然现有经典数学分析和集合论解决了许多实际的“无穷事物”定量认知问题,但也产生了许多性质完全相同的、专门暴露相同基础理论致命缺陷的各种悬而未决的悖论家族“.抽象事物—抽象事物的载体”为基础的新无穷理论体系和系统性的“无穷载体理论”的构建,为我们开辟了一条解决现有经典集合论和数学分析基础理论中的三个缺陷及其相关悖论的新思路,决定了第四代数学分析和第二代无穷集合论的产生.Starting from the most primitive basis,our studies have proved that the un-scientific defined and contradictory concepts of“potential infinite-actual infinite”have been the foundation of present classical infinite theory system,this leads to the fact that both present classical mathematical analysis and set theory have exactly three same fundamental defects since ancient times,because they have been basing on the same classical infinite theory system.It is true that both present classical mathematical analysis and set theory have solved many practical quantitative cognizing problems to many“infinite things”in our science,but they produced many suspended paradoxes at the same time.The construction of new infinite theory system basing on“abstract things-the carriers of abstract things”and the development of the systematic theory of“infinite carriers”open up a new working way to solve the three fundamental defects in old generations of infinite set theory and mathematical analysis and decides the productions of the forth generation of mathematical analysis and the second generation of set theory.The“number forms with half Archimedean property”was defined and a new definition of infinite set was given.

关 键 词：“无穷事物” 定量认知 无穷悖论综合症 潜无穷—实无穷 新无穷理论体系 “无穷载体”理论 “半阿基米德性” 第四代数学分析和第二代无穷集合论 

分 类 号：N02[自然科学总论—科学技术哲学] O143[理学—数学]