What question did this study set out to answer?

This essay aims to critique the arguments claiming that infinite sets differ in size and expose their fallacious nature.

June 19, 2026Open Access

Cantor's fallacy from semantic pathologies in mathematics

Key Points

This essay aims to critique the arguments claiming that infinite sets differ in size and expose their fallacious nature.
Analyzed standard arguments regarding infinite sets.
Identified logical inconsistencies in these arguments.
Questioned the definition of output for non-terminating functions.
Demonstrated that arguments about differing magnitudes of infinite sets lead to contradictions.
Challenged the notion that a non-terminating function can have a finite output.

Abstract

This essay examines the standard arguments used to claim that infinite sets can differ in magnitude, exposing a fallacious form of reasoning that permits the derivation of contradictory conclusions, and calling into question the ontological legitimacy of attributing a defined final output to a non-terminating function.

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Cite This Study

Iván Alfredo Solana (Sun,) studied this question.

synapsesocial.com/papers/6a34df4a65a5b0777af2e73d https://doi.org/https://doi.org/10.5281/zenodo.20723669