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An inconsistent table of natural numbers

Author:

Leon, Antonio

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

February 19, 2021

File:

/Research Papers-Mathematics and Applied Mathematics/Download/8393

Downloads:

145

Keywords:

d-modular row, d-exchanges, w-order, actual infinity, potential infinity, Axiom of Infinity.

Abstract:

This paper proves the existence of a class of natural numbers that can be used to reorder the rows of a table that contains all natural numbers in such a way that all of its rows become d-modular, a concept this paper also introduces. The existence of such a reordering contradicts the fact that infinitely many rows of the table can never become d-modular. The corresponding proofs are so basic and simple that only foundational elements of set theory can be involved in the contradiction.