Mathematics and Applied Mathematics
July 31, 2020
d-modular row, d-exchange, w-order, actual infinity, potential infinity, Axiom of Infinity
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.