Kaoru, Takamatsu (2024) Identification of numbers with operators to construct cardinals. [Preprint]

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Abstract

This article describes confirmation of the two propositions: (1) a set of operators to construct cardinals satisfies Peano Axioms, hence the set is identified with the natural numbers, and (2) from these operators, three kinds of operators can be derived that are identified with the integers, the fractions, and the complex numbers with fractions as their coefficients respectively. These four kinds of operators stand in a sequential inclusion relationship, in contrast to the embedding relationship between those kinds of numbers that are identified with sets. This article describes confirmation of two propositions: (1) a set of operators to construct cardinals satisfies Peano Axioms , hence the set is identified with the natural numbers, and (2) these operators can be extended to form three kinds of operators that are identified with the integers, the fractions and the complex numbers with fractions as their coefficients, respectively. These four kinds of operators stand in a sequential inclusion relationship, in contrast to the embedding relationship between numbers that are identified with sets.

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Item Type:	Preprint
Creators:	Creators Email ORCID Kaoru, Takamatsu ckeyv910@sutv.zaq.ne.jp 0000-0002-6146-1308
Keywords:	numbers; operators; cardinals, structures of sets; iteration; activation.
Subjects:	Specific Sciences > Mathematics > Foundations General Issues > Confirmation/Induction Specific Sciences > Mathematics General Issues > Theory Change
Depositing User:	Mr. Kaoru Takamatsu
Date Deposited:	18 Jul 2024 16:35
Last Modified:	18 Jul 2024 16:35
Item ID:	23708
Subjects:	Specific Sciences > Mathematics > Foundations General Issues > Confirmation/Induction Specific Sciences > Mathematics General Issues > Theory Change
Date:	29 June 2024
URI:	https://philsci-archive.pitt.edu/id/eprint/23708

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• Identification of numbers with operators to construct cardinals. (deposited 01 Jul 2024 18:33)
  • Identification of numbers with operators to construct cardinals. (deposited 18 Jul 2024 16:35) [Currently Displayed]

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