Real numbers, continued fractions and complexity classes
type: Item
instance of: scholarly article
title: Real numbers, continued fractions and complexity classes
zbMATH Open document ID: 0715.03026
DOI: 10.1016/0168-0072(90)90052-4
author: Salah Labhalla
author: Henri Lombardi
published in: Annals of Pure and Applied Logic
publication date: 1990-01-01T00:00:00Z
review text: Some representations of real numbers (including Cauchy sequences of rationals, Dedekind cuts and variants, and continued fractions) are studied from both the viewpoint of recursive functionals and of complexity theory. Complexity arguments are used also to make explicit the impossibility of obtaining some functions as recursive functionals. It is also shown that representations of real numbers that are equivalent from the viewpoint of recursive functionals are clearly different from the viewpoint of complexity. Continued fractions are studied in a more detailed way. The authors claim that Cauchy sequences of rationals are ``the unique representation of real numbers suitable for the ordinary calculus''.
Mathematics Subject Classification ID: 03F60
Mathematics Subject Classification ID: 03D15
Mathematics Subject Classification ID: 26E40
Mathematics Subject Classification ID: 11A55
zbMATH DE Number: 4177051
zbMATH Keywords: representations of real numbers
zbMATH Keywords: Cauchy sequences of rationals
zbMATH Keywords: Dedekind cuts
zbMATH Keywords: continued fractions
zbMATH Keywords: recursive functionals
reviewed by: Pier Luigi Ferrari
MaRDI profile type: Publication
full work available at URL: 0168-0072(90)90052-4
OpenAlex ID: W1995082015
cites work: Q5727752
cites work: Q5812175
cites work: On the definitions of some complexity classes of real numbers
cites work: Corrigenda to: ``On the continued fraction representation of computable real numbers''
cites work: Recursive Real Numbers
cites work: Simple continued fractions for some irrational numbers. II
cites work: Nicht konstruktiv beweisbare Sätze der Analysis
cites work: On Computable Numbers, with an Application to the Entscheidungsproblem
Wikidata QID: Q127554402
description: scientific article; zbMATH DE number 4177051