Proceedings of the 2025 9th International Seminar on Education, Management and Social Sciences (ISEMSS 2025)

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The Construction of Real Numbers from Rational Numbers in Elementary Mathematics Establishes Their Infinite Existence

Authors
Peilong Zhang1, *
1School of Mathematical Sciences, University of Jinan, Shandong, Jinan, 250022, China
*Corresponding author. Email: ss_zhangpl@ujn.edu.cn
Corresponding Author
Peilong Zhang
Available Online 12 September 2025.
DOI
10.2991/978-2-38476-462-4_82How to use a DOI?
Keywords
Elementary Mathematics; Rational Numbers; Irrational Numbers; Constructive Method; Denseness
Abstract

This article delves into several core conclusions related to the density of real numbers, employing constructive methods to provide rigorous proofs. The overall thought process is clear, the logic is stringent, and the language is simple and easy to understand, aiming to offer readers an intuitive and profound way of understanding. Through specific constructive examples, the article not only showcases the unique charm of constructive methods in proving the density of real numbers but also further reveals the intrinsic structure and properties of the real number system. Whether for mathematics students or for the general mathematics enthusiasts, this article has certain reference value and inspirational significance.

Copyright
© 2025 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Volume Title
Proceedings of the 2025 9th International Seminar on Education, Management and Social Sciences (ISEMSS 2025)
Series
Advances in Social Science, Education and Humanities Research
Publication Date
12 September 2025
ISBN
978-2-38476-462-4
ISSN
2352-5398
DOI
10.2991/978-2-38476-462-4_82How to use a DOI?
Copyright
© 2025 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

risenwbib
TY  - CONF
AU  - Peilong Zhang
PY  - 2025
DA  - 2025/09/12
TI  - The Construction of Real Numbers from Rational Numbers in Elementary Mathematics Establishes Their Infinite Existence
BT  - Proceedings of the 2025 9th International Seminar on Education, Management and Social Sciences (ISEMSS 2025)
PB  - Atlantis Press
SP  - 736
EP  - 742
SN  - 2352-5398
UR  - https://doi.org/10.2991/978-2-38476-462-4_82
DO  - 10.2991/978-2-38476-462-4_82
ID  - Zhang2025
ER  -