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

Ramon Carbó Dorca; Carlos Perelman

doi:10.33187/jmsm.972781

EN

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

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.

Keywords

Boolean Hypercubes, Collatz conjecture, Collatz vector spaces, Mersenne numbers, Natural hypercubes

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Ramon Carbó Dorca ^*
0000-0002-9219-0686
Spain

Carlos Perelman
0000-0002-7276-9957
United States

Publication Date

December 1, 2022

Submission Date

July 17, 2021

Acceptance Date

September 16, 2022

Published in Issue

Year 2022 Volume: 5 Number: 3

DOI

https://doi.org/10.33187/jmsm.972781

IZ

https://izlik.org/JA49XU63MN

APA

Carbó Dorca, R., & Perelman, C. (2022). Boolean Hypercubes, Classification of Natural Numbers, and the Collatz Conjecture. Journal of Mathematical Sciences and Modelling, 5(3), 80-91. https://doi.org/10.33187/jmsm.972781

AMA

1.Carbó Dorca R, Perelman C. Boolean Hypercubes, Classification of Natural Numbers, and the Collatz Conjecture. Journal of Mathematical Sciences and Modelling. 2022;5(3):80-91. doi:10.33187/jmsm.972781

Chicago

Carbó Dorca, Ramon, and Carlos Perelman. 2022. “Boolean Hypercubes, Classification of Natural Numbers, and the Collatz Conjecture”. Journal of Mathematical Sciences and Modelling 5 (3): 80-91. https://doi.org/10.33187/jmsm.972781.

EndNote

Carbó Dorca R, Perelman C (December 1, 2022) Boolean Hypercubes, Classification of Natural Numbers, and the Collatz Conjecture. Journal of Mathematical Sciences and Modelling 5 3 80–91.

IEEE

[1]R. Carbó Dorca and C. Perelman, “Boolean Hypercubes, Classification of Natural Numbers, and the Collatz Conjecture”, Journal of Mathematical Sciences and Modelling, vol. 5, no. 3, pp. 80–91, Dec. 2022, doi: 10.33187/jmsm.972781.

ISNAD

Carbó Dorca, Ramon - Perelman, Carlos. “Boolean Hypercubes, Classification of Natural Numbers, and the Collatz Conjecture”. Journal of Mathematical Sciences and Modelling 5/3 (December 1, 2022): 80-91. https://doi.org/10.33187/jmsm.972781.

JAMA

1.Carbó Dorca R, Perelman C. Boolean Hypercubes, Classification of Natural Numbers, and the Collatz Conjecture. Journal of Mathematical Sciences and Modelling. 2022;5:80–91.

MLA

Carbó Dorca, Ramon, and Carlos Perelman. “Boolean Hypercubes, Classification of Natural Numbers, and the Collatz Conjecture”. Journal of Mathematical Sciences and Modelling, vol. 5, no. 3, Dec. 2022, pp. 80-91, doi:10.33187/jmsm.972781.

Vancouver

1.Ramon Carbó Dorca, Carlos Perelman. Boolean Hypercubes, Classification of Natural Numbers, and the Collatz Conjecture. Journal of Mathematical Sciences and Modelling. 2022 Dec. 1;5(3):80-91. doi:10.33187/jmsm.972781