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The identification of numbers with operators

Takamatsu, Kaoru (2025) The identification of numbers with operators. [Preprint]

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Abstract

Abstract
This article describes confirmation of the proposition that numbers are identified with operators in the following three steps. 1. The set of operators to construct finite cardinals satisfies Peano Axioms. 2. Accordingly, the natural numbers can be identified with these operators. 3. From the operators, five kinds of operators are derived, and on the basis of the step 2, the integers, the fractions, the real numbers, the complex numbers and the quaternions are identified with the five kinds of operators respectively. These operators stand in a sequential inclusion relationship, in contrast to the embedding relationship between those kinds of numbers defined as sets.

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Item Type: Preprint
Creators:
CreatorsEmailORCID
Takamatsu, Kaoruckeyv910@sutv.zaq.ne.jp0000-0002-6146-1308
Keywords: numbers; operators; cardinals; structures of sets; iteration; activation.
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics
General Issues > Philosophers of Science
Depositing User: Mr. Kaoru Takamatsu
Date Deposited: 02 Apr 2025 17:41
Last Modified: 02 Apr 2025 17:41
Item ID: 24968
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics
General Issues > Philosophers of Science
Date: 28 March 2025
URI: https://philsci-archive.pitt.edu/id/eprint/24968

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