Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 13, 30 November 2023
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Delving into the continuum hypothesis: A thorough examination of set theory and the nuances of mathematical infinity
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Abstract
This essay delves deep into one of the most intriguing mathematical puzzles of all time: the Continuum Hypothesis. Beginning with a robust foundational exploration, it sheds light on the key concepts of cardinality and power sets, which are pivotal to the realm of set theory. These foundational ideas set the stage for a deeper investigation into the relationship that the Continuum Hypothesis shares with real numbers and natural numbers. Historically, the Continuum Hypothesis has tantalized mathematicians. This paper takes a journey through time, highlighting the various endeavors to either prove or refute this hypothesis. Some of the most brilliant minds have grappled with its complexities, leaving behind a rich tapestry of mathematical thought. Furthermore, a significant portion of our discussion is centered on situating the Continuum Hypothesis within the context of Zermelo-Fraenkel Set Theory (ZFC). The intricate interplay between the hypothesis and ZFC offers profound insights and raises thought-provoking questions about the very nature of mathematical truth.
Keywords
Continuum Hypothesis, Set Theory, Cardinality, Power Sets, Zermelo-Fraenkel Set Theory
References
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4. Han, & van Doorn, F. (2021). A Formal Proof of the Independence of the Continuum Hypothesis. https://doi.org/10.1145/3372885.3373826.
5. Link, M. (2022). The Dispute between Two Accounts of the Continuum. The Journal of Philosophy, 119(8), 425-443.
6. Sonar, T., & Sonar, T. (2021). At the Turn to the 20th Century: Set Theory and the Search for the True Continuum. 3000 Years of Analysis: Mathematics in History and Culture, 537-600.
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Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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- Volume Title
- Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
- ISBN (Print)
- 978-1-83558-189-6
- ISBN (Online)
- 978-1-83558-190-2
- Published Date
- 30 November 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/13/20240813
- Copyright
- 30 November 2023
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited