Kaoru, Takamatsu (2024) Identification of numbers with operators to construct cardinals. [Preprint]
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Abstract
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 | ||||||
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| 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 |
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| Depositing User: | Mr. Kaoru Takamatsu | ||||||
| Date Deposited: | 01 Jul 2024 18:33 | ||||||
| Last Modified: | 01 Jul 2024 18:33 | ||||||
| Item ID: | 23653 | ||||||
| Subjects: | Specific Sciences > Mathematics > Foundations General Issues > Confirmation/Induction Specific Sciences > Mathematics General Issues > Theory Change |
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| Date: | 29 June 2024 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/23653 |
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