数学季刊 ›› 2013, Vol. 28 ›› Issue (1): 41-46.

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数学无穷与中介逻辑(上)——Leibniz的割线与切线问题在中介逻辑中的逻辑数学解释方法

  

  1. 1. School of Information Science and Technology, Nanjing University of Aeronautics and Astronautics 2. State Key Laboratory of Software Development Environment, Beihang University 3. School of Electronics and Information Engineering, Nanjing University of Technology 4. Institute of Modern Logic and Applications, Nanjing University

  • 收稿日期:2011-03-02 出版日期:2013-03-30 发布日期:2023-03-07
  • 作者简介:ZHU Wu-jia(1934-), male, native of Yixing, Jiangsu, a professor of Nanjing University of Aeronautics and Astronautics, engages in logic, mathematic foundation and computer science; GONG Ning-sheng(1958-), male, native of Nanjing, Jiangsu, a professor of Nanjing University of Technology, engages in logic and computer science.
  • 基金资助:
    Supported by the Open Fund of the State Key Laboratory of Software Development Environment(SKLSDE-2011KF-04)； Supported by the National High Technology Research and Development Program of China (863 Program)(2009AA043303)

Mathematical Infinity and Medium Logic (I) —Logical-mathematical Interpretation of Leibniz’s Secant and Tangent Lines Problem  in Medium Logic

  1. 1. School of Information Science and Technology, Nanjing University of Aeronautics and Astronautics 2. State Key Laboratory of Software Development Environment, Beihang University 3. School of Electronics and Information Engineering, Nanjing University of Technology 4. Institute of Modern Logic and Applications, Nanjing University

  • Received:2011-03-02 Online:2013-03-30 Published:2023-03-07
  • About author:ZHU Wu-jia(1934-), male, native of Yixing, Jiangsu, a professor of Nanjing University of Aeronautics and Astronautics, engages in logic, mathematic foundation and computer science; GONG Ning-sheng(1958-), male, native of Nanjing, Jiangsu, a professor of Nanjing University of Technology, engages in logic and computer science.
  • Supported by:
    Supported by the Open Fund of the State Key Laboratory of Software Development Environment(SKLSDE-2011KF-04)； Supported by the National High Technology Research and Development Program of China (863 Program)(2009AA043303)

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摘要： From the perspective of potential infinity (poi) and actual infinity, Ref [4] has confirmed that poi and aci are in ’unmediated opposition’ (P,﹁P ) whether in ZFC or not; it has further been proved that the manners in which a variable infinitely approaches its limit also satisfy the law of intermediate exclusion. With these results as theoretical bases, this paper attempts to provide an accurate and strict logical-mathematical interpretation of the incompatibility of Leibniz’s secant and tangent lines in the medium logic system from the perspective of logical mathematics. 

关键词: calculus, limit theory, medium logic, potential infinity, actual infinity

Abstract: From the perspective of potential infinity (poi) and actual infinity, Ref [4] has confirmed that poi and aci are in ’unmediated opposition’ (P,﹁P ) whether in ZFC or not; it has further been proved that the manners in which a variable infinitely approaches its limit also satisfy the law of intermediate exclusion. With these results as theoretical bases, this paper attempts to provide an accurate and strict logical-mathematical interpretation of the incompatibility of Leibniz’s secant and tangent lines in the medium logic system from the perspective of logical mathematics. 

Key words: calculus, limit theory, medium logic, potential infinity, actual infinity

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