Survey Article: The real numbers–A survey of constructions

2015/06/01 by Ittay Weiss · 5 citations
Computer Science · Mathematics · #Algebra over a field #Arithmetic #Computability, Logic, AI Algorithms #Discrete mathematics #Epistemology #History and Theory of Mathematics #Logic, programming, and type systems #Mathematics #Mathematics education #Pure mathematics #Rational number #Real number #Simple (philosophy)

paper · pdf · doi:10.1216/rmj-2015-45-3-737

published in Rocky Mountain Journal of Mathematics 45(3) (Rocky Mountain Mathematics Consortium)

openalex publication_date 2015/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/21

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

• The real numbers as a wreath product
• Defining reals without the use of rationals
• Two concrete new constructions of the real numbers
• Stevin numbers and reality

Cited by

• Construction of the real numbers [wikipedia]

Related

• The real numbers - a survey of constructions
• A new approach to the real numbers
• Rationally Querying the Reals
• Unified Approach to Real Numbers in Various Mathematical Settings
• A natural construction for the real numbers