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.
| Published in | American Journal of Applied Mathematics (Volume 8, Issue 4) |
| DOI | 10.11648/j.ajam.20200804.16 |
| Page(s) | 216-222 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2020. Published by Science Publishing Group |
Natural Number Set, Real Number Set, Set Potential, Continuity Problem, Mixed Potential, Hyperfinite Theory, Infinite Classification
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APA Style
Zhu Rongrong. (2020). From the Continuity Problem of Set Potential to Georg Cantor Conjecture. American Journal of Applied Mathematics, 8(4), 216-222. https://doi.org/10.11648/j.ajam.20200804.16
ACS Style
Zhu Rongrong. From the Continuity Problem of Set Potential to Georg Cantor Conjecture. Am. J. Appl. Math. 2020, 8(4), 216-222. doi: 10.11648/j.ajam.20200804.16
AMA Style
Zhu Rongrong. From the Continuity Problem of Set Potential to Georg Cantor Conjecture. Am J Appl Math. 2020;8(4):216-222. doi: 10.11648/j.ajam.20200804.16
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Download@article{10.11648/j.ajam.20200804.16,
author = {Zhu Rongrong},
title = {From the Continuity Problem of Set Potential to Georg Cantor Conjecture},
journal = {American Journal of Applied Mathematics},
volume = {8},
number = {4},
pages = {216-222},
doi = {10.11648/j.ajam.20200804.16},
url = {https://doi.org/10.11648/j.ajam.20200804.16},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20200804.16},
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.},
year = {2020}
}
TY - JOUR T1 - From the Continuity Problem of Set Potential to Georg Cantor Conjecture AU - Zhu Rongrong Y1 - 2020/07/28 PY - 2020 N1 - https://doi.org/10.11648/j.ajam.20200804.16 DO - 10.11648/j.ajam.20200804.16 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 216 EP - 222 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20200804.16 AB - 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. VL - 8 IS - 4 ER -
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