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From the Continuity Problem of Set Potential to Georg Cantor Conjecture
American Journal of Applied Mathematics
Volume 8, Issue 4, August 2020, Pages: 216-222
Received: May 8, 2020; Accepted: Jul. 13, 2020; Published: Jul. 28, 2020
Author
Zhu Rongrong, DIEG Mathematics Research of HR, Fudan University, Shanghai, China
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Abstract
Background in 1878, Cantor puted forward his famous conjecture. Cantor's famous conjecture is whether there is continuity between the potential of the set of natural numbers and the potential of the set of real numbers. In 1900, Hilbert puted forward the first question of 23 famous mathematical problems at the International Congress of mathematicians in Paris. Purpose To study the continuity of set potential between the natural number set and the real number set, so as to provide mathematical support for the study of male gene fragment in human genome. Method The potential is extended by infinite division of sets and differential incremental equilibrium theory. There is a symmetry relation that the smallest element of infinite partition is 2. When a set A corresponds to a subset of a set B one by one, but it can't make A correspond to B one by one, the potential of A is said to be smaller than that of B. If a is the potential of A, and b is the potential of B, then a < b. We use ∼•0 to express the potential of natural number set and ∼•1 to express the potential of real number set. At present, it is not known whether there is a set X, the potential of X satisfies ∼•0 < x < ∼•1. Results There is no continuity problem in the set potential of the natural number set and the real number set, and four mixed potentials can be formed. It belongs to the category of super finite theory. Conclusion Cantor's conjecture is proved that potential of the natural number set and the real number set. That is, the potential of X satisfies ∼̇ 0 < x < ∼̇ 1 does not exist.
Keywords
Natural Number Set, Real Number Set, Set Potential, Continuity Problem, Mixed Potential, Hyperfinite Theory, Infinite Classification
Zhu Rongrong, From the Continuity Problem of Set Potential to Georg Cantor Conjecture, American Journal of Applied Mathematics. Vol. 8, No. 4, 2020, pp. 216-222. doi: 10.11648/j.ajam.20200804.16
References
[1]
Zhang Wenxiu, Qiu Guofang, Uncertain Decision Making Based on Rough Sets, Beijing China, tsinghua university press, 2005: 1-255.
[2]
Zheng Weiwei, Complex Variable Function and Integral Transform, Northwest Industrial University Press, 2011: 1-396.
[3]
Lou Senyue, Tang Xiaoyan, Nonlinear Mathematical Physics Method, Beijing China, Science Press, 2006: 1-365.
[4]
Zhu Rongrong, Differential Incremental Equilibrium Theory, Fudan University, Vol 1, 2007: 1-213.
[5]
LABPHTEB M. A., TriaBAT B. B., Methods of Function of a Complex Variable Originally published in Russian under the title, 1956, 2006: 1-287.
[6]
Numerical Treatment of Multi-Scale Problems Porceedings of the 13th GAMM-Seminar, Kiel, January 24-26, 1997 Notes on Numerical Fluid Mechanics Volume 70 Edited By WolfGangHackBusch and Gabriel Wittum.
[7]
Zhu Rongrong, Differential Incremental Equilibrium Theory, Fudan University, Vol 2, 2008: 1-352.
[8]
C. Rogers W. K. Schief, Bäcklund and Darboux Transformations: Geometry and Modern Applications in SolitionTheory, first published by Cambridge University, 2015: 1-292.
[9]
Gu chaohao, Hu Hesheng, Zhou Zixiang, DarBoux Transformation in Solition Theory and Its Geometric Applications (The second edition), Shanghai science and technology Press, 1999, 2005: 1-271.
[10]
W. Miller, Symmetry Group and Its Application, Beijing China, Science Press, 1981: 1-486.
[11]
Gong Sheng, Harmonic Analysis on Typical Groups Monographs on pure mathematics and Applied Mathematics Number twelfth, Beijing China, Science Press, 1983: 1-314.
[12]
Ren Fuyao, Complex Analytic Dynamic System, Shanghai China, Fudan University Press, 1996: 1-364.
[13]
Chen Zhonghu, Lie group guidance, Higher Education Press, 1997: 1-334.
[14]
Su Jingcun, Topology of Manifold, Wuhan China, wuhan university press, 2005: 1-708.
[15]
Wu Chuanxi, Li Guanghan, Submanifold geometry, Beijing China, Science Press, 2002: 1-217.
[16]
Ding Peizhu, Wang Yi, Group and its Express, Higher Education Press, 1999: 1-468.
[17]
Zheng jianhua, Meromorphic Functional Dynamics System, Beijing China, tsinghua university press, 2006: 1-413.
[18]
Xiao Gang, Fibrosis of Algebraic Surfaces, Shanghai China, Shanghai science and technology Press, 1992: 1-180.
[19]
Jari Kaipio Erkki Somersalo, Statistical and Computational Inverse Problems With 102 Figures, Spinger.
[20]
E. M. Chirka, Complex Analytic Sets Mathematics and Its Applications, Kluwer Academic Publishers Gerald Karp, Cell and Molecular Biology: Concepts and Experiments (3e), Higher Education Press, 2005: 1-792.
[21]
Qiu Chengtong, Sun Licha, Differential Geometry Monographs on pure mathematics and Applied Mathematics Number eighteenth, Beijing China, Science Press, 1988: 1-403.
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