The Novel Whole Number Classification and the 3 to 2 Ratio

Grounded in a novel mathematical framework, this study partitions the set of whole numbers (ℕ0) into four distinct hierarchical classes. A key innovation is the definition of Ultimate Numbers—the union of the prime numbers with zero and one—which resolves classic conceptual limitations. Three further subsets, representing increasing degrees of numerical complexity, are subsequently defined by the initial distinction between ultimate and non-ultimate numbers within ℕ0. The structural interaction among these four classes yields unique arithmetic arrangements in their initial distribution, most notably revealing an exact and recurring 3:2 ratio.