Set Theory and Logic

2510 Submissions

[2] viXra:2510.0149 [pdf] submitted on 2025-10-30 20:23:19

Scale-Relative Set Theory: A Unified Foundation for Mathematics and Physics

Authors: Daniel Nehmé
Comments: 15 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We introduce Scale-Relative Set Theory (SRST), a revolutionary framework where mathematical concepts are inherently relative to observational scales $kappa in mathbb{E}$. This theory naturally resolves classical paradoxes (Russell, Cantor, Burali-Forti), unifies arithmetic with geometry through a fundamental number-point isomorphism, and provides new foundations for topology, analysis, and modern physics. We develop complete scale-relative constructions of numerical sets, set operations, distance metrics, and neighborhood systems. The framework demonstrates profound connections to gauge theories, parallel transport, renormalization group flow, and quantum gravity. SRST explains how mathematical structures emerge across scales from quantum to cosmological, offering a unified understanding of reality that transforms both mathematical foundations and physical theory.
Category: Set Theory and Logic

[1] viXra:2510.0098 [pdf] replaced on 2025-12-26 18:42:33

Intuition and Game Shows

Authors: Richard L. Hudson
Comments: 6 Pages.

The game show problem originated when Steve Selvin submitted his paper 'A Problem in Probability' to 'The American Statistician' magazine Feb 1975. [1] After receiving some negative reviews from readers, he submitted a 2nd letter to the editor Aug 1975. [1] There was little public awareness of his game show analysis until 1990, when Craig Whitaker posed a question of a winning strategy for a similar game show to Marilyn Savant who wrote articles for Parade magazine.The debate of probability of success as 2/3 vs 1/2 has continued until today.This paper reveals a common error in both Selvin and Savant interpretations.
Category: Set Theory and Logic