Set Theory and Logic

Constructing the Real Numbers R by Rejecting Bijections on Infinite Sets

Authors: Chang Hee Kim
Comments: 100 Pages. License CC BY (Note by ai.viXra.org Admin: For the last time, please cite listed scientific references)leased under Creative Commons CC BY 4.0 license.

This paper introduces a constructive definition of the real numbers R derived directly from the non-negative integers Z. Each real number is defined as a definite and finite value, represented either by a finite sum or by a generative, convergent process of rationals. By rejecting bijection between infinite sets—the core assumption underlying Cantorian set theory—the proposed framework eliminates self-contradictions inherent in ZFC and resolves classical paradoxes in set theory, measure theory, and topology. The result is a coherent, contradiction-free foundation for analysis that restores mathematics to constructive logic and physical intelligibility.
Category: Set Theory and Logic