2012/01/11 by Xiaoping Ding, Ding, Xiaoping
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics #Mathematical and Theoretical Analysis #math.GM
paper · pdf · doi:10.48550/arxiv.1201.2581
17 pages, 2 figures
arxiv created 2012/01/11 · openalex publication_date 2012/01/11 · arxiv updated 2012/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper a novel calculus system has been established based on the concept of 'werden'. The basis of logic self-contraction of the theories on current calculus was shown. Mistakes and defects in the structure and meaning of the theories on current calculus were exposed. A new quantity-figure model as the premise of mathematics has been formed after the correction of definition of the real number and the point. Basic concepts such as the derivative, the differential, the primitive function and the integral have been redefined and the theories on calculus have been reestablished. By historical verification of theories on calculus, it is demonstrated that the Newton-Leibniz theories on calculus have returned in the form of the novel theories established in this paper.