| ai.viXra.org > Set Theory and Logic > 2511 |
|
 |
| ai.viXra.org > Set Theory and Logic > 2511 |
|
|
[2] ai.viXra.org:2511.0044 [pdf] submitted on 2025-11-14 21:35:32
Authors: Alin Setar
Comments: 4 Pages.
This paper presents a critical review of Chang Hee Kim’s 2025 preprint, "Cantor’s Continuum Hypothesis Is Proved Wrong" (ai.viXra:2505.0211v1). The work proposes an alternative approach to infinite cardinality by decomposing the set of natural numbers into infinitely many symmetric subsets. We examine the logical structure of Kim’s argument, the role of "infinite decomposition," and its implications for Cantor’s diagonal method and the Continuum Hypothesis (CH). In particular, we demonstrate that Kim’s framework operates outside the standard Zermelo—Fraenkel set theory with the Axiom of Choice (ZFC), since it redefines core notions such as bijection, power set, and cardinality.
Category: Set Theory and Logic
[1] ai.viXra.org:2511.0026 [pdf] submitted on 2025-11-09 00:02:23
Authors: Jianbo Li
Comments: 4 Pages. Degenerates from quantization methods to classical equations
This paper investigates the proposition of natural number addition, $1 + 1 = 2$. First, a rigorous proof using the classical CSUM method is presented within the frameworks of set theory and the Peano axioms. Next, the traditional proof based on formal logic by Bertrand Russell and Alfred North Whitehead in textit{Principia Mathematica} is reviewed. Finally, the two approaches are compared in detail, analyzing their differences in conceptual approach, complexity, and scalability, and discussing the advantages of the CSUM method in terms of algebraic intuition and category-theoretic extensions. This study aims to demonstrate how modern methods can complement traditional formal logic, thereby enriching perspectives on foundational mathematics research.
Category: Set Theory and Logic