The real numbers - a survey of constructions

2015/05/18 by Ittay Weiss, Weiss, Ittay · 1 citation
Computer Science · Mathematics · #00A05 #Computability, Logic, AI Algorithms #FOS: Mathematics #History and Overview (math.HO) #Logic, programming, and type systems #math.HO #msc:00A05 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1506.03467

arxiv created 2015/05/18 · openalex publication_date 2015/05/18 · arxiv updated 2015/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts to recent results, and allowing for a simple comparison-at-a-glance between different constructions.

Citations

• A new construction of the real numbers by alternating series
• The real numbers as a wreath product

Cited by

• Real numbers as infinite decimals -- theory and computation

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