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June 11, 2026Open Access

The Structure and Quantity of Real Numbers V.2

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Authors

LMLaerte Ferreira MorgadoFederal Senate

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Implication

This work demonstrates a new understanding of real numbers refuting Cantor's claims, impacting set theory and logic.

Key Points

  • This work aims to challenge Cantor's theorems on the uncountability of real numbers and propose alternative interpretations.
  • Presented concepts and theorems related to the structure of real numbers.
  • Analyzed the distribution patterns of rational and irrational numbers along the real number line.
  • Provided interpretations and refutations of Cantor's diagonal argument.
  • Demonstrated a regular interleaving of rational and irrational numbers, suggesting equal sizes of these sets.
  • Refuted Cantor's theorem on uncountability, implying the hierarchy of infinities in set theory is incorrect.
  • Indicated that the Continuum Hypothesis would hold vacuously due to false antecedent conditions.

Cite This Study

Laerte Ferreira Morgado (2026) studied this question.

synapsesocial.com/papers/6a2a52ae80c8f91e7f39e8f8https://doi.org/10.5281/zenodo.20615763
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Cantor's Diagonal Argument: Uncountable Reals, Hierarchy of Infinities, Uncomputable Functions — E8 Intelligence Research2026
  2. 2Real Numbers Are Countably Infinite: The Fatal Defects of Cantor's Diagonal Argument and the Constructive Complexity Alternative2026
  3. 3Diagonalization Links Cantor's Infinity Hierarchy to Gödel's Incompleteness — E8 Intelligence Research2026
  4. 4Wittgenstein on Cantor’s Proof2025
  5. 5Unfolding Infinity: Fractal Counterarguments to Cantorian Formalism2025 · 1 citations