TY  - JOUR
T1  - Boolean Hypercubes, Classification of Natural Numbers, and the Collatz Conjecture
AU  - Carbó Dorca, Ramon
AU  - Perelman, Carlos
PY  - 2022
DA  - December
Y2  - 2022
DO  - 10.33187/jmsm.972781
JF  - Journal of Mathematical Sciences and Modelling
PB  - Mahmut AKYİĞİT
WT  - DergiPark
SN  - 2636-8692
SP  - 80
EP  - 91
VL  - 5
IS  - 3
LA  - en
AB  - 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.
KW  - Boolean Hypercubes
KW  - Collatz conjecture
KW  - Collatz vector spaces
KW  - Mersenne numbers
KW  - Natural hypercubes
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UR  - https://doi.org/10.33187/jmsm.972781
L1  - https://dergipark.org.tr/en/download/article-file/1885797
ER  -