Set Theory and Logic

2211 Submissions

[4] viXra:2211.0122 [pdf] submitted on 2022-11-21 01:18:43

Proof of the Existence of Dark Numbers

Authors: Wolfgang Mückenheim
Comments: 8 Pages. In English and German

We will prove by means of Cantor's mapping between natural numbers and positive fractions that his approach to actual infinity implies the existence of numbers which cannot be applied as defined individuals. We will call them dark numbers.
Category: Set Theory and Logic

[3] viXra:2211.0102 [pdf] submitted on 2022-11-17 11:20:31

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

Authors: Nhat-Anh Phan
Comments: 15 Pages. Copyright. All rights reserved.

For a given infinite countable set constituted by the union of infinitely many non-empty, finite or infinite countable, disjoint sub-sets A = {i∈N*}[A_i]_P(A) , ∀i ∈ N* , A_i ≠ ∅, ∀i, j ∈ N* , i ≠ j, A_i ∩ A_j = ∅, we demonstrate that it is legitimate to partition A in a finite or infinite number of sub-sets that are themselves constituted by a finite or infinite number of sub-sets of A when the initial order of indexation of the sub-sets of A maintains a strictly increasing order in each sub-set.
Category: Set Theory and Logic

[2] viXra:2211.0091 [pdf] replaced on 2022-12-12 14:00:40

On Problems and Their Solution Spaces

Authors: Theophilus Agama
Comments: 6 Pages. An important correction has been made in the definition of problem space.

We introduce and develop the logic of existence of solution to problems. We use this theory to answer the question of Florentin Smarandache in logic. We answer this question in the negative.
Category: Set Theory and Logic

[1] viXra:2211.0060 [pdf] replaced on 2024-02-29 23:29:09

Proof of the Lemma About the Absence of Nontrivial Cycles Collatz Sequences

Authors: Savinov Sergey
Comments: 2 Pages.

The article provibes an outline of the proof of the absence of nontrivial cycles in the Collatz sequence.
Category: Set Theory and Logic