Set Theory and Logic

2308 Submissions

[3] viXra:2308.0150 [pdf] submitted on 2023-08-23 00:33:20

A Proof of a Conjecture of lu Concerning Inequality for the Gamma Function

Authors: CholMyong Song, TaeHyon Mun, YongIl Han, WonChol Kim, HyonChol Kim
Comments: 6 Pages.

Dawei Lu [Dawei Lu, A generated approximation related to Burnside’s formula, Journal of Number Theory 136 (2014) 414—422; http://dx.doi.org/10.1016/j.jnt.2013.10.016] proposed a conjecture: for every real number k>0, there exists depending k, such that for every, it holds: He guessed that it is suitable for taking = 0.5. In this paper, we prove the conjecture of Dawei Lu.
Category: Set Theory and Logic

[2] viXra:2308.0146 [pdf] submitted on 2023-08-23 00:17:02

One Third Crucial Theorem for the Refoundation of Elementary Set Theory and the Teaching of that Discipline to Future Generations

Authors: Nhat-Anh Phan
Comments: 22 Pages. In French - Copyright All rights reserved

For a given infinite countable set A, we demonstrate that A is an infinite countableset if and only if A is equal to an infinite countable set indexed to the infinity. Saidotherwise we demonstrate that A is an infinite countable set iff there exists an infinite numberof non-empty, distinct elements a_i ǂ ∅, i ∈ N∗, ∀i, j ∈ N∗, i ǂ j, a_i ǂ a_j such thatA = U_{+∞}_{i=1} {a_i}. At this occasion, for infinite countable sets constituted by the union of two giveninfinite countable sets A and B, Au2032 = [A ∪ B]P(Au2032), we introduce the notion of undeterminedinfinite countable set in order to designate infinite countable sets for whichan explicit indexation is not determined meanwhile such indexation must necessarilyexist.
Category: Set Theory and Logic

[1] viXra:2308.0058 [pdf] submitted on 2023-08-11 22:44:16

Categorifying Connections

Authors: Ryan J. Buchanan
Comments: 5 Pages.

The notion of a connection from differential geometry is employed in a category-theoretic context. We discuss the properties of holonomy from a tangent ∞-category perspective.
Category: Set Theory and Logic