What question did this study set out to answer?

Identify foundational defects in Cantor's diagonal argument and establish a constructive alternative demonstrating that real numbers are countably infinite.

August 19, 2026Open Access

Real Numbers Are Countably Infinite: The Fatal Defects of Cantor's Diagonal Argument and the Constructive Complexity Alternative

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SLSheng Lu

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Implication

Theoretical analysis demonstrates countable infinity of real numbers within a Moebius-fiber topology framework, challenging Cantor's diagonal proof of uncountability.

Key Points

Identify foundational defects in Cantor's diagonal argument and establish a constructive alternative demonstrating that real numbers are countably infinite.
Evaluated Cantor's diagonal argument within the framework of Bu Theory to assess computability boundaries and set-theoretic cardinality.
Constructed a set-theoretic surjection framework from natural numbers to real numbers using Möbius-fiber topology.
Analyzed spacing ratios and critical state behavior across ten experimental groups with complete numerical data.
Demonstrated constructive countability of real numbers across ten numerical experimental groups via a valid surjection framework.
Found that activating the fiber operator at critical state p=1 engages the GUE repulsion kernel, shifting the spacing ratio from 1/e ≈ 0.368 to ≈ 0.599.

Cite This Study

Sheng Lu (2026) studied this question.

synapsesocial.com/papers/6a85639d03308d306e2d6e76 https://doi.org/10.5281/zenodo.21980629

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Implication

Theoretical analysis demonstrates countable infinity of real numbers within a Moebius-fiber topology framework, challenging Cantor's diagonal proof of uncountability.

Real Numbers Are Countably Infinite: The Fatal Defects of Cantor's Diagonal Argument and the Constructive Complexity Alternative

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Implication

Key Points

Cite This Study

Real Numbers Are Countably Infinite: The Fatal Defects of Cantor's Diagonal Argument and the Constructive Complexity Alternative

Discussion

Member takes

Implication

Key Points

Cite This Study

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