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Numerical consequences of the inconsistent infinity

Author:

Leon, Antonio

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

September 10, 2025

File:

/Research Papers-Mathematics and Applied Mathematics/Download/10308

Downloads:

103

Keywords:

Actual Infinity, potential infinity, axiom of infinity, complete totality, natural numbers, integer numbers, rational numbers, irrational numbers, real numbers.

Abstract:

This article analyzes the formal consequences of the inconsistent actual infinity on certain types of numbers and numerical sets. These results are so strong that I have not included them in this abstract to prevent some readers from abandoning their careful reading of the article at this point. They are the results that can be expected when the existence of a formal object that has always been discussed — the actual infinite — is axiomatically accepted without discussion for over a century. A type of infinity whose inconsistency can be demonstrated simply by using the tools provided by the new infinitist mathematics built upon it.

Comments

J. Zwarts(Netherlands):

e, pi, sqrt(2) are numbers which cannot be expressed as m/n with m and n natural numbers.
So they are not elements of Q, the set of rational numbers.
They are called irrational numbers.

Posted: September 11, 2025 @ 11:14:37 am

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