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Number – the Basic Concept of Mathematics

Author:

Voytsekhovsky, Vladimir Vladimirovich

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

April 29, 2026

File:

/Research Papers-Mathematics and Applied Mathematics/Download/10533

Downloads:

Keywords:

philosophy of mathematics, unit, number, natural numbers

Abstract:

The article briefly considers the approaches to the definition of the concept of number by the scientists of Ancient Greece, Aristotle, Frege, Peano, Russell, Dedekind and modern science. The author of this paper proposes basic concept of “tsel” to define the concepts of “unit” and “natural number”, and it is shown that the participation of a reasonable subject is necessary in the formation of the concepts of “unit” and “number”. Also, the properties of fractional (rational) numbers are considered; it is shown that the reason for the appearance of infinite rational numbers is the use of a specific number system, for example, decimal and the resulting incommensurability of some natural numbers, which manifests itself in the fact that it is impossible, for example, to answer the question: “How many numbers a (for example, the number a=7) is contained in the number b (for example, the number b=10). The properties of irrational numbers are considered.

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