{"id":"https://openalex.org/W2762493074","doi":"https://doi.org/10.3233/com-170081","title":"On subrecursive representability of irrational numbers, part II","display_name":"On subrecursive representability of irrational numbers, part II","publication_year":2017,"publication_date":"2017-10-10","ids":{"openalex":"https://openalex.org/W2762493074","doi":"https://doi.org/10.3233/com-170081","mag":"2762493074"},"language":"en","primary_location":{"id":"doi:10.3233/com-170081","is_oa":true,"landing_page_url":"https://doi.org/10.3233/com-170081","pdf_url":"https://content.iospress.com:443/download/computability/com081?id=computability%2Fcom081","source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://content.iospress.com:443/download/computability/com081?id=computability%2Fcom081","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063909629","display_name":"Lars Kristiansen","orcid":"https://orcid.org/0000-0002-6749-4004"},"institutions":[{"id":"https://openalex.org/I184942183","display_name":"University of Oslo","ror":"https://ror.org/01xtthb56","country_code":"NO","type":"education","lineage":["https://openalex.org/I184942183"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"Lars Kristiansen","raw_affiliation_strings":["Departments of Mathematics and Informatics, University of Oslo, PO Box 1053, Blindern, NO-0316 Oslo, Norway. larsk@math.uio.no"],"affiliations":[{"raw_affiliation_string":"Departments of Mathematics and Informatics, University of Oslo, PO Box 1053, Blindern, NO-0316 Oslo, Norway. larsk@math.uio.no","institution_ids":["https://openalex.org/I184942183"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5063909629"],"corresponding_institution_ids":["https://openalex.org/I184942183"],"apc_list":null,"apc_paid":null,"fwci":0.9511,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.78353861,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"8","issue":"1","first_page":"43","last_page":"65"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9876999855041504,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/irrational-number","display_name":"Irrational number","score":0.946247935295105},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.7163619995117188},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7012978792190552},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.602838397026062},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5450364947319031},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5100293755531311},{"id":"https://openalex.org/keywords/base-change","display_name":"Base change","score":0.4594702124595642},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4443073868751526},{"id":"https://openalex.org/keywords/dedekind-cut","display_name":"Dedekind cut","score":0.428619921207428},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3806840777397156},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3469439744949341},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10629403591156006},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10212793946266174}],"concepts":[{"id":"https://openalex.org/C94931360","wikidata":"https://www.wikidata.org/wiki/Q607728","display_name":"Irrational number","level":2,"score":0.946247935295105},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.7163619995117188},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7012978792190552},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.602838397026062},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5450364947319031},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5100293755531311},{"id":"https://openalex.org/C103751382","wikidata":"https://www.wikidata.org/wiki/Q4866384","display_name":"Base change","level":2,"score":0.4594702124595642},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4443073868751526},{"id":"https://openalex.org/C76449584","wikidata":"https://www.wikidata.org/wiki/Q851333","display_name":"Dedekind cut","level":2,"score":0.428619921207428},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3806840777397156},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3469439744949341},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10629403591156006},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10212793946266174},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3233/com-170081","is_oa":true,"landing_page_url":"https://doi.org/10.3233/com-170081","pdf_url":"https://content.iospress.com:443/download/computability/com081?id=computability%2Fcom081","source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"},{"id":"pmh:oai:www.duo.uio.no:10852/61543","is_oa":true,"landing_page_url":"http://hdl.handle.net/10852/61543","pdf_url":null,"source":{"id":"https://openalex.org/S4306401716","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2211-3568","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3233/com-170081","is_oa":true,"landing_page_url":"https://doi.org/10.3233/com-170081","pdf_url":"https://content.iospress.com:443/download/computability/com081?id=computability%2Fcom081","source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5299999713897705,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2762493074.pdf","grobid_xml":"https://content.openalex.org/works/W2762493074.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W293447284","https://openalex.org/W1501334285","https://openalex.org/W1972276887","https://openalex.org/W1975452830","https://openalex.org/W1995082015","https://openalex.org/W2015272527","https://openalex.org/W2020164082","https://openalex.org/W2025476736","https://openalex.org/W2033642714","https://openalex.org/W2144393342","https://openalex.org/W2186805718","https://openalex.org/W2295875602","https://openalex.org/W2472462801","https://openalex.org/W2611511037","https://openalex.org/W2616606085","https://openalex.org/W3022059637","https://openalex.org/W4231629838","https://openalex.org/W4243563333","https://openalex.org/W4245102239","https://openalex.org/W4298287102"],"related_works":["https://openalex.org/W4390041478","https://openalex.org/W4310560878","https://openalex.org/W2999337086","https://openalex.org/W2039091908","https://openalex.org/W4292347539","https://openalex.org/W3142859449","https://openalex.org/W1540764979","https://openalex.org/W3183570752","https://openalex.org/W2762493074","https://openalex.org/W3216821872"],"abstract_inverted_index":{"We":[0,73,83],"consider":[1],"various":[2],"ways":[3],"to":[4,95],"represent":[5],"irrational":[6,12,55],"numbers":[7,56],"by":[8,17,21,29,61,78,88,97],"subrecursive":[9,42],"functions.":[10,51],"An":[11],"number":[13],"can":[14,58],"be":[15,38,59],"represented":[16],"its":[18,22,30],"base-b":[19,23,31,89],"expansion;":[20],"sum":[24,32,92],"approximation":[25,33],"from":[26,34,63],"below;":[27],"and":[28,69,81,91,100],"above.":[35],"Let":[36],"S":[37,64],"a":[39],"class":[40],"of":[41,54],"functions,":[43],"e.g.,":[44],"the":[45,48,67,70,75],"clas":[46],"s":[47],"primitive":[49],"recursive":[50],"The":[52],"set":[53],"that":[57],"obtained":[60,77],"functions":[62],"depends":[65],"on":[66],"representation":[68],"base":[71],"b.":[72],"compare":[74],"sets":[76],"different":[79],"representations":[80,87,96],"bases.":[82],"also":[84],"discuss":[85],"how":[86],"expansions":[90],"approximations":[93],"relate":[94],"Cauchy":[98],"sequences":[99],"Dedekind":[101],"cuts.":[102]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-02T15:55:50.835912","created_date":"2025-10-10T00:00:00"}
