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