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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 or the computable reals or recursive reals. Equivalent definitions can be given using μ-recursive functions, Turing machines, or λ-calculus as the formal representation of algorithms. The computable numbers form a real closed field and can be used in the place of real numbers for many, but not all, mathematical purposes.

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rdf:type	plant
rdfs:label	Computable number (en)
rdfs:comment	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 or the computable reals or recursive reals. Equivalent definitions can be given using μ-recursive functions, Turing machines, or λ-calculus as the formal representation of algorithms. The computable numbers form a real closed field and can be used in the place of real numbers for many, but not all, mathematical purposes. (en)
sameAs	Computable number
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Cite_journal dbt:Cite_web dbt:Cn dbt:Quote dbt:Refbegin dbt:Refend dbt:Reflist dbt:Sfnp dbt:Short_description dbt:Number_systems
Subject	Computability theory Theory of computation
Link from a Wikipage to an external page	https://github.com/blambov/RealLib http://eccc.uni-trier.de/static/books/A_Simple_Introduction_to_Computable_Analysis_Fragments_of_a_Book/ http://doc.rero.ch/record/304204/files/S0022481200105663.pdf https://books.google.com/books%3Fid=KqeXZ4pPd5QC&pg=PA363 https://books.google.com/books%3Fid=oN5nsPkXhhsC http://www.abelard.org/turpap2/tp2-ie.asp https://eudml.org/doc/281227 https://archive.org/details/computationfinit0000mins
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gold:hypernym	Numbers
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Wikipage revision ID	1072601550 (xsd:integer)
Link from a Wikipage to another Wikipage	Rounding Uncountable set Undecidable problem Well-ordering principle Alan Turing Algebraic number Algorithm Almost all Approximation error Bijection Semicomputable function Turing degree Turing machine Universal Turing machine Modulus of convergence Bounded function Cantor's diagonal argument Computability theory Theory of computation General recursive function Surjective function Chaitin's constant Cube root Decision problem Dedekind cut Definable real number Dense order Hyperarithmetical theory Complex number Computable analysis Computable function Computably enumerable Constructible number Constructivism (philosophy of mathematics) Countable set Henry Gordon Rice Homeomorphism Order isomorphism Partial function Specker sequence Ernst Specker Errett Bishop Field (mathematics) Gödel numbering Halting problem Infimum and supremum Injective function Integer Lambda calculus Transcendental number Transcomputational problem Subcountability Totally disconnected space Marvin Minsky Mathematics Measure (mathematics) History of numbers Nested intervals Rational number Real closed field Real number dbr:Computable_algebra
has abstract	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 or the computable reals or recursive reals. Equivalent definitions can be given using μ-recursive functions, Turing machines, or λ-calculus as the formal representation of algorithms. The computable numbers form a real closed field and can be used in the place of real numbers for many, but not all, mathematical purposes. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Computable_number
is Wikipage redirect of	Non-computable number Non-computable numbers Noncomputable number

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