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Computable number

In mathematics, computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm. They are also known as the recursive numbers, effective numbers, computable reals, or recursive reals. The concept of a computable real number was introduced by Émile Borel in 1912, using the intuitive notion of…

Applications, Properties & Formal definition

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Overview

Informal definition

Formal definition

Properties

Non-computable numbers

Digit strings and the Cantor and Baire spaces

Use in place of the reals

Implementations of exact arithmetic

Advanced semantic analysis

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Map overview Semantic statistics

Computable number

Nodes69
Edges68
Triples52
Avg. degree1.97
Density0.028986
Components1

How this topic connects Entity context

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Computable number

Top relations

related to Non-computability of the ordering · 13
Computable number → Dedekind, It, Let, NO, That, The, Then, This, Thus, To, Turing, While, YES
related to Not computably enumerable · 12
Computable number → Assigning, But, Cantor's, Consequently, Gödel, Here, In, The, There, This, Turing, While
related to Use in place of the reals · 7
Computable number → For, Russian, Specker, The, This, Though, To
related to Non-computable numbers · 5
Computable number → Chaitin's, Every, Omega, There, Turing
related to Other properties · 5
Computable number → Despite, Ernst Specker, For, Specker, The
related to Properties as a field · 4
Computable number → Henry Gordon Rice, The, These, Turing
related to Digit strings and the Cantor and Baire spaces · 2
Computable number → The, Turing's

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Important terminology

computable numbers displaystyle real number turing machine reals definition decimal function epsilon omega given set field equivalent produces sequence digit

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
theseinstance ofDespite the existence of counterexamples0.80text
parts of calculusinstance ofDespite the existence of counterexamples0.80text
real analysis can be developed in the field of computable numbersinstance ofDespite the existence of counterexamples0.80text
leading to the study of computable analysis.The set of computable real numbersinstance ofDespite the existence of counterexamples0.80text
Computable numberrelated to Digit strings and the Cantor and Baire spacesTuring's0.60section
Computable numberrelated to Digit strings and the Cantor and Baire spacesThe0.60section
Computable numberrelated to Non-computability of the orderingThe0.60section
Computable numberrelated to Non-computability of the orderingLet0.60section
Computable numberrelated to Non-computability of the orderingTuring0.60section
Computable numberrelated to Non-computability of the orderingThen0.60section
Computable numberrelated to Non-computability of the orderingYES0.60section
Computable numberrelated to Non-computability of the orderingNO0.60section

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