{"id":"https://openalex.org/W4230270700","doi":"https://doi.org/10.1007/978-1-4471-0717-0_16","title":"Monotonically Computable Real Numbers","display_name":"Monotonically Computable Real Numbers","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W4230270700","doi":"https://doi.org/10.1007/978-1-4471-0717-0_16"},"language":"en","primary_location":{"id":"doi:10.1007/978-1-4471-0717-0_16","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4471-0717-0_16","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Computability and Logic","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076334612","display_name":"Robert Rettinger","orcid":null},"institutions":[{"id":"https://openalex.org/I120691247","display_name":"FernUniversit\u00e4t in Hagen","ror":"https://ror.org/04tkkr536","country_code":"DE","type":"education","lineage":["https://openalex.org/I120691247"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Robert Rettinger","raw_affiliation_strings":["FernUniversit\u00e4t Hagen, Hagen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"FernUniversit\u00e4t Hagen, Hagen, Germany","institution_ids":["https://openalex.org/I120691247"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102089636","display_name":"Xizhong Zheng","orcid":null},"institutions":[{"id":"https://openalex.org/I51783024","display_name":"Brandenburg University of Technology Cottbus-Senftenberg","ror":"https://ror.org/02wxx3e24","country_code":"DE","type":"education","lineage":["https://openalex.org/I51783024"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Xizhong Zheng","raw_affiliation_strings":["BTU Cottbus, Cottbus, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"BTU Cottbus, Cottbus, Germany","institution_ids":["https://openalex.org/I51783024"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030136295","display_name":"Romain Gengler","orcid":null},"institutions":[{"id":"https://openalex.org/I51783024","display_name":"Brandenburg University of Technology Cottbus-Senftenberg","ror":"https://ror.org/02wxx3e24","country_code":"DE","type":"education","lineage":["https://openalex.org/I51783024"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Romain Gengler","raw_affiliation_strings":["BTU Cottbus, Cottbus, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"BTU Cottbus, Cottbus, Germany","institution_ids":["https://openalex.org/I51783024"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051107719","display_name":"Burchard von Braunm\u00fchl","orcid":null},"institutions":[{"id":"https://openalex.org/I51783024","display_name":"Brandenburg University of Technology Cottbus-Senftenberg","ror":"https://ror.org/02wxx3e24","country_code":"DE","type":"education","lineage":["https://openalex.org/I51783024"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Burchard von Braunm\u00fchl","raw_affiliation_strings":["BTU Cottbus, Cottbus, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"BTU Cottbus, Cottbus, Germany","institution_ids":["https://openalex.org/I51783024"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8408,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.76562033,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"187","last_page":"201"},"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/T11567","display_name":"semigroups and automata theory","score":0.9703999757766724,"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":0.9588000178337097,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.8546302914619446},{"id":"https://openalex.org/keywords/computable-number","display_name":"Computable number","score":0.838770866394043},{"id":"https://openalex.org/keywords/rational-number","display_name":"Rational number","score":0.626767098903656},{"id":"https://openalex.org/keywords/computable-function","display_name":"Computable function","score":0.6197677254676819},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5987077355384827},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5977503061294556},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5886141061782837},{"id":"https://openalex.org/keywords/computable-analysis","display_name":"Computable analysis","score":0.5856918096542358},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.5663673281669617},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5508794188499451},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5160650610923767},{"id":"https://openalex.org/keywords/real-analysis","display_name":"Real analysis","score":0.49377331137657166},{"id":"https://openalex.org/keywords/gap-theorem","display_name":"Gap theorem","score":0.4651333689689636},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45606932044029236},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07909929752349854}],"concepts":[{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.8546302914619446},{"id":"https://openalex.org/C156382255","wikidata":"https://www.wikidata.org/wiki/Q818895","display_name":"Computable number","level":4,"score":0.838770866394043},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.626767098903656},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.6197677254676819},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5987077355384827},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5977503061294556},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5886141061782837},{"id":"https://openalex.org/C27318111","wikidata":"https://www.wikidata.org/wiki/Q5157264","display_name":"Computable analysis","level":3,"score":0.5856918096542358},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.5663673281669617},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5508794188499451},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5160650610923767},{"id":"https://openalex.org/C1911482","wikidata":"https://www.wikidata.org/wiki/Q854531","display_name":"Real analysis","level":2,"score":0.49377331137657166},{"id":"https://openalex.org/C3853638","wikidata":"https://www.wikidata.org/wiki/Q1314081","display_name":"Gap theorem","level":5,"score":0.4651333689689636},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45606932044029236},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07909929752349854},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"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/C81150689","wikidata":"https://www.wikidata.org/wiki/Q1217677","display_name":"Fundamental theorem of calculus","level":4,"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/C206929604","wikidata":"https://www.wikidata.org/wiki/Q530152","display_name":"Picard\u2013Lindel\u00f6f theorem","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-1-4471-0717-0_16","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4471-0717-0_16","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Computability and Logic","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1497475168","https://openalex.org/W1545819195","https://openalex.org/W1552949294","https://openalex.org/W1638251065","https://openalex.org/W1994458535","https://openalex.org/W2007775665","https://openalex.org/W2145295071","https://openalex.org/W4231629838","https://openalex.org/W4232277851","https://openalex.org/W4254793172","https://openalex.org/W6737131063"],"related_works":["https://openalex.org/W2150482238","https://openalex.org/W197714092","https://openalex.org/W2527631632","https://openalex.org/W2007775665","https://openalex.org/W1498085647","https://openalex.org/W2080359559","https://openalex.org/W4206028083","https://openalex.org/W2046021909","https://openalex.org/W4241646449","https://openalex.org/W4206289504"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}