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- Gödel_numbering_for_sequences abstract "In mathematics, a Gödel numbering for sequences provides us an effective way to represent each finite sequence of natural numbers as a single natural number. Of course, the embedding is surely possible set theoretically, but the emphasis is on the effectiveness of the functions manipulating such representations of sequences: the operations on sequences (accessing individual members, concatenation) can be \"implemented\" using total recursive functions, and in fact by primitive recursive functions.It is usually used to build sequential “data types” in the realm of arithmetic-based formalizations of some fundamental notions of mathematics. It is a specific case of the more general idea of Gödel numbering.E.g. recursive function theory can be regarded as a formalization of notion “algorithm”, and if we regard it as a programming language, we can mimic arrays, lists by encoding a sequence of natural numbers in a single natural number — to achieve this, we can use various number theoretic ideas. Using the fundamental theorem of arithmetic is a straightforward way, but there are also more economic approaches, e.g. using the pairing function combined with the Chinese remainder theorem in a sophisticated way.".
- Gödel_numbering_for_sequences wikiPageExternalLink ~csirmaz.
- Gödel_numbering_for_sequences wikiPageExternalLink whyfp.html.
- Gödel_numbering_for_sequences wikiPageExternalLink fo_arith.html.
- Gödel_numbering_for_sequences wikiPageExternalLink l10.ps.gz.
- Gödel_numbering_for_sequences wikiPageExternalLink whyfp.html.
- Gödel_numbering_for_sequences wikiPageID "8371092".
- Gödel_numbering_for_sequences wikiPageLength "23125".
- Gödel_numbering_for_sequences wikiPageOutDegree "69".
- Gödel_numbering_for_sequences wikiPageRevisionID "705831158".
- Gödel_numbering_for_sequences wikiPageWikiLink Abstraction.
- Gödel_numbering_for_sequences wikiPageWikiLink Abuse_of_notation.
- Gödel_numbering_for_sequences wikiPageWikiLink Algorithm.
- Gödel_numbering_for_sequences wikiPageWikiLink Analogy.
- Gödel_numbering_for_sequences wikiPageWikiLink Bijection.
- Gödel_numbering_for_sequences wikiPageWikiLink Category:Articles_containing_proofs.
- Gödel_numbering_for_sequences wikiPageWikiLink Category:Computability_theory.
- Gödel_numbering_for_sequences wikiPageWikiLink Chinese_remainder_theorem.
- Gödel_numbering_for_sequences wikiPageWikiLink Code_reuse.
- Gödel_numbering_for_sequences wikiPageWikiLink Computable_function.
- Gödel_numbering_for_sequences wikiPageWikiLink Congruence_relation.
- Gödel_numbering_for_sequences wikiPageWikiLink Constructive_proof.
- Gödel_numbering_for_sequences wikiPageWikiLink Coprime_integers.
- Gödel_numbering_for_sequences wikiPageWikiLink Data_type.
- Gödel_numbering_for_sequences wikiPageWikiLink Definition.
- Gödel_numbering_for_sequences wikiPageWikiLink Divisor.
- Gödel_numbering_for_sequences wikiPageWikiLink Equality_(mathematics).
- Gödel_numbering_for_sequences wikiPageWikiLink Existential_quantification.
- Gödel_numbering_for_sequences wikiPageWikiLink Factorial.
- Gödel_numbering_for_sequences wikiPageWikiLink Fundamental_theorem_of_arithmetic.
- Gödel_numbering_for_sequences wikiPageWikiLink Gödel_numbering.
- Gödel_numbering_for_sequences wikiPageWikiLink Implementation.
- Gödel_numbering_for_sequences wikiPageWikiLink Injective_function.
- Gödel_numbering_for_sequences wikiPageWikiLink Interface_(computing).
- Gödel_numbering_for_sequences wikiPageWikiLink Irreducible_element.
- Gödel_numbering_for_sequences wikiPageWikiLink List_(abstract_data_type).
- Gödel_numbering_for_sequences wikiPageWikiLink Markov_algorithm.
- Gödel_numbering_for_sequences wikiPageWikiLink Mathematics.
- Gödel_numbering_for_sequences wikiPageWikiLink Modular_arithmetic.
- Gödel_numbering_for_sequences wikiPageWikiLink Modular_programming.
- Gödel_numbering_for_sequences wikiPageWikiLink Mutual_exclusivity.
- Gödel_numbering_for_sequences wikiPageWikiLink Number_theory.
- Gödel_numbering_for_sequences wikiPageWikiLink Pairing_function.
- Gödel_numbering_for_sequences wikiPageWikiLink Pattern_matching.
- Gödel_numbering_for_sequences wikiPageWikiLink Prenex_normal_form.
- Gödel_numbering_for_sequences wikiPageWikiLink Prime_element.
- Gödel_numbering_for_sequences wikiPageWikiLink Primitive_recursive_function.
- Gödel_numbering_for_sequences wikiPageWikiLink Programming_language.
- Gödel_numbering_for_sequences wikiPageWikiLink Projection_(mathematics).
- Gödel_numbering_for_sequences wikiPageWikiLink Propositional_calculus.
- Gödel_numbering_for_sequences wikiPageWikiLink Reductio_ad_absurdum.
- Gödel_numbering_for_sequences wikiPageWikiLink Remainder.
- Gödel_numbering_for_sequences wikiPageWikiLink Specification_(technical_standard).
- Gödel_numbering_for_sequences wikiPageWikiLink Transitive_relation.
- Gödel_numbering_for_sequences wikiPageWikiLink Turing_machine.
- Gödel_numbering_for_sequences wikiPageWikiLink Typeful_programming.
- Gödel_numbering_for_sequences wikiPageWikiLink Uniqueness_quantification.
- Gödel_numbering_for_sequences wikiPageWikiLink Zero_of_a_function.
- Gödel_numbering_for_sequences wikiPageWikiLink Μ-recursive_function.
- Gödel_numbering_for_sequences wikiPageWikiLink Μ_operator.
- Gödel_numbering_for_sequences wikiPageWikiLinkText "Gödel number".
- Gödel_numbering_for_sequences wikiPageWikiLinkText "Gödel numbering for sequences".
- Gödel_numbering_for_sequences wikiPageWikiLinkText "Gödel numbering".
- Gödel_numbering_for_sequences wikiPageUsesTemplate Template:Cite_book.
- Gödel_numbering_for_sequences wikiPageUsesTemplate Template:Cite_journal.
- Gödel_numbering_for_sequences wikiPageUsesTemplate Template:Main.
- Gödel_numbering_for_sequences wikiPageUsesTemplate Template:See_also.
- Gödel_numbering_for_sequences subject Category:Articles_containing_proofs.
- Gödel_numbering_for_sequences subject Category:Computability_theory.
- Gödel_numbering_for_sequences type Diacritic.
- Gödel_numbering_for_sequences type Proof.
- Gödel_numbering_for_sequences type Redirect.
- Gödel_numbering_for_sequences type Thing.
- Gödel_numbering_for_sequences comment "In mathematics, a Gödel numbering for sequences provides us an effective way to represent each finite sequence of natural numbers as a single natural number.".
- Gödel_numbering_for_sequences label "Gödel numbering for sequences".
- Gödel_numbering_for_sequences seeAlso Gxc3xb6dels_xcexb2_function.
- Gödel_numbering_for_sequences sameAs Q5626453.
- Gödel_numbering_for_sequences sameAs m.02712_8.
- Gödel_numbering_for_sequences sameAs Q5626453.
- Gödel_numbering_for_sequences wasDerivedFrom Gödel_numbering_for_sequences?oldid=705831158.
- Gödel_numbering_for_sequences isPrimaryTopicOf Gödel_numbering_for_sequences.