Revising The Concept of Natural Numbers

Natural numbers, or whole numbers, understood abstractly as primarily numbers such as 3, 8, 5, 9, 12, and so on, are a fascinating concept. However, are they the only valid way of understanding and examining the concept of natural or whole numbers? The paper will attempt to revise natural numbers by removing their special formal status, as merely convenient and practical numbers representing amounts whole to themselves, emphasizing the concept that a number, representing an amount, is whole to itself. By examining the possibility of their revision as mere convenient numbers equal in formal value to other numbers as amounts representing themselves as wholes, the understanding of numbers and their values, both formal and informal, may be developed as an exercise in a combination of the properties of numbers and philosophical thought, a combination of elementary arithmetic as including the basic numbers, and of metaphysics regarding the nature of numbers in our reality.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-16
DOI
https://doi.org/10.5281/zenodo.20709349
Primary Topic
History and Theory of Mathematics
Type
preprint
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preprint

Revising The Concept of Natural Numbers

Aku L. T. Jutila
Zenodo (CERN European Organization for Nuclear Research)
History and Theory of Mathematics
preprint

Revising The Concept of Natural Numbers

Aku L. T. Jutila
preprint en

Abstract

Natural numbers, or whole numbers, understood abstractly as primarily numbers such as 3, 8, 5, 9, 12, and so on, are a fascinating concept. However, are they the only valid way of understanding and examining the concept of natural or whole numbers? The paper will attempt to revise natural numbers by removing their special formal status, as merely convenient and practical numbers representing amounts whole to themselves, emphasizing the concept that a number, representing an amount, is whole to itself. By examining the possibility of their revision as mere convenient numbers equal in formal value to other numbers as amounts representing themselves as wholes, the understanding of numbers and their values, both formal and informal, may be developed as an exercise in a combination of the properties of numbers and philosophical thought, a combination of elementary arithmetic as including the basic numbers, and of metaphysics regarding the nature of numbers in our reality.

Zenodo (CERN European Organization for Nuclear Research)
History and Theory of Mathematics
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