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A Constructive Challenge to the Continuum Hypothesis via Fractional and Irrational Set Union

17 October 2025, Version 1
Working Paper
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

This paper proposes a novel set construction that challenges the Continuum Hypothesis (CH), which posits that no set exists with cardinality strictly between that of the integers Z and the real numbers R. The set T is defined as: T={1/2,1/3,1/4,… } ∪ {2/3, 2/5, 2/7,…} ∪ {3/2, 3/4, 3/5, …} ∪ (irrational subset) This union includes:

Keywords

Cardinality
Fractional Sets
Irrational Numbers
Zermelo–Fraenkel Axioms
Mathematical Logic
Infinity
Countable vs Uncountable
Philosophical Mathematics

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Version History

Oct 17, 2025 Version 1

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License

All Rights Reserved

DOI

10.33774/coe-2025-p5209
D O I: 10.33774/coe-2025-p5209 [opens in a new tab]

Author’s competing interest statement

The author(s) have declared they have no conflict of interest with regard to this content

Ethics

The author(s) have declared ethics committee/IRB approval is not relevant to this content

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