数学悖论与数学发展关系分析  

Analysis on the relationship between mathematical paradox and mathematical development

作　　者：王锦瑞 张亚娣 WANG Jinrui;ZHANG Yadi(School of Mathematics and Statics,Shaanxi Xueqian Normal University,Xi′an 710100,China;Shangqiu Minzhu Road No.2 Primary School,Shangqiu 476000,China)

机构地区：[1]陕西学前师范学院数学与统计学院,陕西西安710100 [2]商丘市民主路第二小学,河南商丘476000

出　　处：《高师理科学刊》2022年第9期22-25,共4页Journal of Science of Teachers＇College and University

基　　金：国家社会科学基金项目(18BTJ014)。

摘　　要：基于数学悖论的定义,探讨了数学悖论对数系、微积分、概率论、集合论、几何学等方面发展的影响,分析了数学悖论在无理数的产生,欧氏几何与非欧几何的发展、概率论的公理化以及微积分基础的完善等各方面发挥的不可替代作用.并由此表明,数学悖论的提出是数学发展过程中的必然产物,它反映出数学的概念、理论体系在当时历史条件下或存在一定漏洞,从而打破了数学思维的惯性及局限性,不断促进新的数学理论体系的产生,进而推动数学的发展与完善.Based on the definition of mathematical paradox,the influence of mathematical paradox on the development of logarithm system,geometry,probability,calculus was discussed.The irreplaceable role of the mathematical paradox was specifically analyzed in the generation of irrational numbers,the development of Euclidean geometry and non Euclidean geometry,the axiomatization of probability theory,and the improvement of the foundation of calculus.it showed that emergence of mathematical paradox is the inevitable outcome in the process of mathematical development,it reflected that the concept and theoretical system of mathematics may have some loopholes under the historical conditions at that time,thus broken the inertia and limitations of mathematical thinking,constantly promoted the emergence of new mathematical theoretical system,and further promoted the development and improvement of mathematics.

关 键 词：数学悖论 贝特朗悖论 罗素悖论 数学发展 

分 类 号：N91[自然科学总论]