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

Year 2022, Volume: 5 Issue: 3, 80 - 91, 01.12.2022

Ramon Carbó Dorca , Carlos Perelman

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

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

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