Boolean Hypercubes, Classification of Natural Numbers, and the Collatz Conjecture

Author:

CARBÓ DORCA Ramon1ORCID,PERELMAN Carlos2

Affiliation:

1. University of Girona

2. Clark Atlanta University

Abstract

Using simple arguments derived from the Boolean hypercube configuration, the structure of natural spaces, and the recursive exponential generation of the set of natural numbers, a linear classification of the natural numbers is presented. The definition of a pseudolinear Collatz operator, the description of the set of powers of $2$, and the construction of the natural numbers via this power set might heuristically prove the Collatz conjecture from an empirical point of view.

Publisher

Journal of Mathematical Sciences and Modelling

Subject

Materials Chemistry,Economics and Econometrics,Media Technology,Forestry

Reference35 articles.

1. [1] R. Carbo-Dorca, Boolean Hypercubes, Mersenne numbers and the Collatz conjecture, J. Math. Sci. Mod., 3 (2020), 120-129.

2. [2] The Collatz conjecture. Wikipedia, https://en.wikipedia.org/wiki/Collatz conjecture “What is the Importance of the Collatz Conjecture?” https://math.stackexchange.com/questions/2694/what-is-the-importanceof-the-collatz-conjecture.

3. [3] H. Nowak, Collatz conjecture and emergent properties, https://www.youtube.com/watch?v=QrzcHhBQ2b0.

4. [4] J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92(1) (1985), 323.

5. [5] J. C. Lagarias, A. Weiss, The 3x+1 problem: two stochastic models, Ann. Applied Prob. 2 (1992), 329-361.

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