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The Axiom of Infinity is Inconsistent

Author:

Leon, Antonio

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

December 12, 2024

File:

/Research Papers-Mathematics and Applied Mathematics/Download/10018

Downloads:

Keywords:

Axiom of Infinity, actual infinity, dense order, spacetime continuum

Abstract:

This article contains the shortest proof I have been able to develop of the inconsistency of the actual infinity and the Axiom of Infinity. The proof is based on the dual numerable and densely ordered nature of the rational interval (0, 1), and is a consequence of assuming that there exist all rational numbers greater than zero and less than 1, without there being a first rational number greater than zero (a similar proof could be based on the assumed existence of all rational number less than 1 without there being a last rational number less than 1).