Set Theory and Logic

2207 Submissions

[3] viXra:2207.0138 [pdf] submitted on 2022-07-24 01:07:50

New Approach to the Hilbert's Hotel Paradox

Authors: Juan Elias Millas Vera
Comments: 2 Pages.

In this short article I wanted to expand the Hilbert’s Grand Hotel Paradox. Building on the first two statements, I add a third, possibly necessary, statement.
Category: Set Theory and Logic

[2] viXra:2207.0090 [pdf] submitted on 2022-07-13 00:23:50

Sampling of Infinite Set by J-sequence: Solving Bertrand's (Chord) Paradox

Authors: Jeonghoon Lee
Comments: 20 Pages.

In an infinite set, probabilities are defined on the structure of the set rather than on individual elements. We should take into account the property of a σ-algebra where probabilities are defined. A σ-algebra is closed under ‘only countable’ unions, and the axioms of probability assume σ-additivity. If this is overlooked, something bizarre could be happened as the proposed three solutions of Bertrand's problem. Bertrand's problem is not a paradox, but well defined(posed). The suggested three solutions have the common problem of dividing the sample space into an uncountably infinite number of sets and treating them equally. If a set is divided into equal(treated) and uncountable infinity, all the divided sets have probability 0, so calculating conditional probabilities with these sets or comparing them with each other becomes meaningless. In a sample space composed of an uncountably infinite number of elements such as [0,1], after calculating the number of cases using the sets(J-sequence m-collection cover) generated by equally dividing the sample space into finite numbers, the probability of an event can be calculated with its limit value(as m becomes infinite). The answer of Bertrand's problem is 1/3.
Category: Set Theory and Logic

[1] viXra:2207.0057 [pdf] submitted on 2022-07-07 23:34:33

The Arrew Theorem Prover

Authors: Boro Sitnikovski
Comments: 1 Page.

Arrew (Arrow Rewriter) is a mathematical system (theorem prover) that allows expressing and working with formal systems. It relies on a simple substitution rule and set equality to derive theorems.
Category: Set Theory and Logic