A new approach to the real numbers

2011/01/10 by Liangpan Li, Li, Liangpan · 1 citation
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #Computability, Logic, AI Algorithms #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1101.1800

openalex publication_date 2011/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we provide a complete approach to the real numbers via decimal representations. Construction of the real numbers by Dedekind cuts, Cauchy sequences of rational numbers, and the algebraic characterization of the real number system by the concept of complete ordered field are also well explained in the new setting.

Citations

• Real numbers as infinite decimals and irrationality of √(2)
• The real numbers as a wreath product

Cited by

• Real numbers as infinite decimals -- theory and computation

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