{"id":"https://openalex.org/W4387477840","doi":"https://doi.org/10.3233/com-230445","title":"Nearly computable real numbers","display_name":"Nearly computable real numbers","publication_year":2023,"publication_date":"2023-10-10","ids":{"openalex":"https://openalex.org/W4387477840","doi":"https://doi.org/10.3233/com-230445"},"language":"en","primary_location":{"id":"doi:10.3233/com-230445","is_oa":true,"landing_page_url":"https://doi.org/10.3233/com-230445","pdf_url":"https://content.iospress.com:443/download/computability/com230445?id=computability%2Fcom230445","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/com230445?id=computability%2Fcom230445","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039739158","display_name":"Peter Hertling","orcid":"https://orcid.org/0000-0002-4442-6711"},"institutions":[{"id":"https://openalex.org/I40527276","display_name":"Universit\u00e4t der Bundeswehr M\u00fcnchen","ror":"https://ror.org/05kkv3f82","country_code":"DE","type":"education","lineage":["https://openalex.org/I1315109972","https://openalex.org/I40527276","https://openalex.org/I4387152969"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Peter Hertling","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Informatik, Universit\u00e4t der Bundeswehr M\u00fcnchen, 85579 Neubiberg, Germany"],"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Informatik, Universit\u00e4t der Bundeswehr M\u00fcnchen, 85579 Neubiberg, Germany","institution_ids":["https://openalex.org/I40527276"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002294022","display_name":"Philip Janicki","orcid":"https://orcid.org/0009-0008-9063-028X"},"institutions":[{"id":"https://openalex.org/I40527276","display_name":"Universit\u00e4t der Bundeswehr M\u00fcnchen","ror":"https://ror.org/05kkv3f82","country_code":"DE","type":"education","lineage":["https://openalex.org/I1315109972","https://openalex.org/I40527276","https://openalex.org/I4387152969"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Philip Janicki","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Informatik, Universit\u00e4t der Bundeswehr M\u00fcnchen, 85579 Neubiberg, Germany"],"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Informatik, Universit\u00e4t der Bundeswehr M\u00fcnchen, 85579 Neubiberg, Germany","institution_ids":["https://openalex.org/I40527276"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039739158"],"corresponding_institution_ids":["https://openalex.org/I40527276"],"apc_list":null,"apc_paid":null,"fwci":0.2015,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56757026,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"13","issue":"1","first_page":"57","last_page":"88"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9782999753952026,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9749000072479248,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computable-analysis","display_name":"Computable analysis","score":0.8875349760055542},{"id":"https://openalex.org/keywords/computable-number","display_name":"Computable number","score":0.8733092546463013},{"id":"https://openalex.org/keywords/computable-function","display_name":"Computable function","score":0.7870620489120483},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7148429155349731},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.6751066446304321},{"id":"https://openalex.org/keywords/cauchy-sequence","display_name":"Cauchy sequence","score":0.5765908360481262},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5542230606079102},{"id":"https://openalex.org/keywords/rational-number","display_name":"Rational number","score":0.5258610248565674},{"id":"https://openalex.org/keywords/computability","display_name":"Computability","score":0.4985172748565674},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46871891617774963},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.4567564129829407},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43883052468299866},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.42355653643608093},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3517839312553406},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0774032473564148}],"concepts":[{"id":"https://openalex.org/C27318111","wikidata":"https://www.wikidata.org/wiki/Q5157264","display_name":"Computable analysis","level":3,"score":0.8875349760055542},{"id":"https://openalex.org/C156382255","wikidata":"https://www.wikidata.org/wiki/Q818895","display_name":"Computable number","level":4,"score":0.8733092546463013},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.7870620489120483},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7148429155349731},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.6751066446304321},{"id":"https://openalex.org/C203192437","wikidata":"https://www.wikidata.org/wiki/Q217847","display_name":"Cauchy sequence","level":2,"score":0.5765908360481262},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5542230606079102},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.5258610248565674},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.4985172748565674},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46871891617774963},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.4567564129829407},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43883052468299866},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.42355653643608093},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3517839312553406},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0774032473564148},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/com-230445","is_oa":true,"landing_page_url":"https://doi.org/10.3233/com-230445","pdf_url":"https://content.iospress.com:443/download/computability/com230445?id=computability%2Fcom230445","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"}],"best_oa_location":{"id":"doi:10.3233/com-230445","is_oa":true,"landing_page_url":"https://doi.org/10.3233/com-230445","pdf_url":"https://content.iospress.com:443/download/computability/com230445?id=computability%2Fcom230445","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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4387477840.pdf","grobid_xml":"https://content.openalex.org/works/W4387477840.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W220096824","https://openalex.org/W1529179093","https://openalex.org/W1566548053","https://openalex.org/W1574049752","https://openalex.org/W1579696469","https://openalex.org/W1972481159","https://openalex.org/W1976647442","https://openalex.org/W1994458535","https://openalex.org/W2007775665","https://openalex.org/W2008273724","https://openalex.org/W2019259942","https://openalex.org/W2034673847","https://openalex.org/W2037917663","https://openalex.org/W2056105126","https://openalex.org/W2087382793","https://openalex.org/W2101323842","https://openalex.org/W2110665728","https://openalex.org/W2168616714","https://openalex.org/W2559927126","https://openalex.org/W3017124157","https://openalex.org/W3166372913","https://openalex.org/W4232277851","https://openalex.org/W4243563333"],"related_works":["https://openalex.org/W2007775665","https://openalex.org/W197714092","https://openalex.org/W1577501449","https://openalex.org/W2295875602","https://openalex.org/W2527631632","https://openalex.org/W2150482238","https://openalex.org/W2962816983","https://openalex.org/W1533694441","https://openalex.org/W4387477840","https://openalex.org/W4317672154"],"abstract_inverted_index":{"We":[0,34,125],"call":[1,54],"a":[2,10,55,64,97,115,136,231,258],"sequence":[3,26,41,66],"[Formula:":[4,22,27,67],"see":[5,23,28,68],"text]":[6,24,29,69],"of":[7,9,42,70,130,167],"elements":[8],"metric":[11],"space":[12],"nearly":[13,47,59,79,91,116,131,202,259],"computably":[14,31,48,80],"Cauchy":[15,49],"if":[16,61],"for":[17],"every":[18,86],"increasing":[19,40],"computable":[20,60,65,87,117,132,143,154,203,209,260],"function":[21],"the":[25,128],"converges":[30,74],"to":[32,75,257],"0.":[33],"show":[35],"that":[36,45,73,85,112,121,127,200,206,248],"there":[37,62,113],"exists":[38,63,114],"an":[39],"rational":[43,71],"numbers":[44,72,134],"is":[46,78,83,90,122,135,207,210],"and":[50,77,93,101,118,140,175,178,216,220,228,235],"unbounded.":[51],"Then":[52],"we":[53,160,229],"real":[56,88,133,137,144,155,204,261],"number":[57,89,120,205],"\u03b1":[58,76],"Cauchy.":[81],"It":[82],"clear":[84],"computable,":[92],"it":[94],"follows":[95],"from":[96],"result":[98,232],"by":[99,163,176,198,233,246],"Downey":[100,234],"LaForte":[102,236],"(":[103,108,165,171,193,237,242],"Theoretical":[104,238],"Computer":[105,239],"Science":[106,240],"284":[107,241],"2002":[109,243],")":[110,173,195,244],"539\u2013555)":[111,245],"left-computable":[119],"not":[123,150,208,217,226],"computable.":[124],"observe":[126],"set":[129,252],"closed":[138,141,151],"field":[139],"under":[142,152],"functions":[145],"with":[146],"open":[147],"domain,":[148],"but":[149],"arbitrary":[153],"functions.":[156],"Among":[157],"other":[158],"things":[159],"strengthen":[161,230],"results":[162],"Hoyrup":[164],"Theory":[166],"Computing":[168],"Systems":[169],"60":[170],"2017":[172],"396\u2013420)":[174],"Stephan":[177],"Wu":[179],"(In":[180],"New":[181],"computational":[182],"paradigms.":[183],"First":[184],"conference":[185],"on":[186],"computability":[187],"in":[188],"Europe,":[189],"CiE":[190],"2005,":[191],"Proceedings":[192],"2005":[194],"461\u2013469":[196],"Springer)":[197],"showing":[199,247],"any":[201],"weakly":[211],"1-generic":[212],"(and,":[213,224],"therefore,":[214,225],"hyperimmune":[215],"Martin-L\u00f6f":[218],"random)":[219],"strongly":[221],"Kurtz":[222],"random":[223],"K-trivial),":[227],"no":[249],"promptly":[250],"simple":[251],"can":[253],"be":[254],"Turing":[255],"reducible":[256],"number.":[262]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-13T14:20:09.374765","created_date":"2025-10-10T00:00:00"}