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Delving into the continuum hypothesis: A thorough examination of set theory and the nuances of mathematical infinity
- 1 University of Nottingham Ningbo China
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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
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Cite this article
Wang,Y. (2023). Delving into the continuum hypothesis: A thorough examination of set theory and the nuances of mathematical infinity. Theoretical and Natural Science,13,130-135.
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Volume title: Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
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