Study on the Sufficient Certification of Cauchy Convergence Criterion

DOI

10.2991/icmmct-17.2017.280How to use a DOI?

Keywords

Cauchy Convergence Criterion, Application study

Abstract

Cauchy criterion is widely used in mathematical analysis, is the basic theory of mathematical analysis. We prove the Cauchy convergence criterion by using the interval proof theorem and the compactness theorem. In most of the research results, the basic theorem of the real number system is proved in a chain-like manner, and finally an argument ring is formed. The proof of the Cauchy criterion is the focus and the difficulty, especially its adequacy. This paper focuses on the Cauchy convergence criterion sufficient proof, the necessity is simple, this paper only gives a proof.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Ming Wan
PY  - 2017/04
DA  - 2017/04
TI  - Study on the Sufficient Certification of Cauchy Convergence Criterion
BT  - Proceedings of the 2017 5th International Conference on Machinery, Materials and Computing Technology (ICMMCT 2017)
PB  - Atlantis Press
SP  - 1484
EP  - 1488
SN  - 2352-5401
UR  - https://doi.org/10.2991/icmmct-17.2017.280
DO  - 10.2991/icmmct-17.2017.280
ID  - Wan2017/04
ER  -