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

Authors : Ramon CARBÓ DORCA, Carlos PERELMAN

Pages : 80-91

Doi:10.33187/jmsm.972781

View : 14 | Download : 5

Publication Date : 2022-12-01

Article Type : Research Paper

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