Set Theory and Logic

Cracks in Logic: Examining the Uncountability of Real Numbers Through Dedekind Cuts and Rational Density

Authors: Kesan Yi
Comments: 3 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)

This paper re-examines the logical consistency between the uncountability of real numbers and their definition via Dedekind cuts. By integrating the fundamental property of the density of rational numbers, we argue that the "one-to-one" mapping between a unique cut and a unique real number imposes a logical constraint that contradicts the magnitude jump from a countable backbone to an uncountable set. We propose that if the ordering and uniqueness of real numbers are to be maintained, the prevailing conclusion of uncountability necessitates a re-evaluation of its foundational defining tools.
Category: Set Theory and Logic