Do you think the "New Whole Numbers Classification" exactly describes the organization of set N ?
Whole numbers are subdivided into these two categories:
- ultimates: an ultimate number not admits any non-trivial divisor (whole number) being less than it.
- non-ultimates: a non-ultimate number admits at least one non-trivial divisor (whole number) being less than it.
Non-ultimate numbers are subdivided into these two categories:
- raiseds: a raised number is a non-ultimate number, power of an ultimate number.
- composites: a composite number is a non-ultimate and not raised number admitting at least two different divisors.
Composite numbers are subdivided into these two categories:
- pure composites: a pure composite number is a non-ultimate and not raised number admitting no raised number as divisor.
- mixed composites: a mixed composite number is a non-ultimate and not raised number admitting at least a raised number as divisor.
From the paper: Preprint New Whole Numbers Classification
Antonio M. Oller-Marcén it allows to merge the sequence of prime numbers with the exotic numbers 0 and 1. And in this case, this category of numbers is opposed in singular arithmetic arrangement to the other categories as illustrated in the article Preprint The ultimate numbers and the 3/2 ratio
To simplify, before there were: 0, 1, primes and composites. With this new classification, now there are just ultimates and non-ultimates.
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