Mathematical Infinity and Medium Logic （II） --Logical-mathematical Interpretation andLogical Analysis of（△y/△x）is Meaningful and dy/dx is the Tangent Slope） in the Context of Medium Logic  

作　　者：ZHU Wu-jia GONG Ning-sheng DU Guo-ping 

机构地区：[1]School of Information Science and Technology, Nanjing University of Aeronautics and Astronau- tics, Nanjing 210016, China State Key Laboratory of Software Development Environment, Beihang University, Beijin9 100191, China [2]School of Electronics and Information Engineering, Nanjing Uni- versity of Technology, Nanjing 210009, China) [3]Institute of Modern Logic and Applications, Nanjing University, Nanjing 210093, China

出　　处：《Chinese Quarterly Journal of Mathematics》2013年第3期360-365,共6页数学季刊（英文版）

摘　　要：Abstract： Ref [5] provides a logical-mathematical explanation of the incompatibility ofLeibniz＇s secant and tangent lines in medium logic. However, the expression （＊）（△y/△x） ismeaningful and dy/dx is the tangent slope） derived from ⑦ and ⑧ in §4 of Ref [5] is unimaginablewithin the framework of two-valued logic, why shouldn＇t the same conflicting concluslon be reached in the medium logic calculus？ This paper has subjected these questions to careful logical analysis, and approached them from the perspective of logical mathematics. As the two approaches have led to the identical conclusion, the paper thereby rigorously and thoroughlv answers these questions.

关 键 词：CALCULUS limit theory medium logic potential infinity actual infinity 

分 类 号：O114[理学—数学]