{"id":"https://openalex.org/W2888112425","doi":"https://doi.org/10.3390/axioms7030059","title":"An Alternative to Real Number Axioms","display_name":"An Alternative to Real Number Axioms","publication_year":2018,"publication_date":"2018-08-21","ids":{"openalex":"https://openalex.org/W2888112425","doi":"https://doi.org/10.3390/axioms7030059","mag":"2888112425"},"language":"en","primary_location":{"id":"doi:10.3390/axioms7030059","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms7030059","pdf_url":"https://www.mdpi.com/2075-1680/7/3/59/pdf?version=1534861653","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/7/3/59/pdf?version=1534861653","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090609662","display_name":"Igor L\u00ed\u0161ka","orcid":null},"institutions":[{"id":"https://openalex.org/I59655833","display_name":"Matej Bel University","ror":"https://ror.org/016e5hy63","country_code":"SK","type":"education","lineage":["https://openalex.org/I59655833"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"Igor L\u00ed\u0161ka","raw_affiliation_strings":["Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovsk\u00e9ho 40, 974 01 Bansk\u00e1 Bystrica, Slovakia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovsk\u00e9ho 40, 974 01 Bansk\u00e1 Bystrica, Slovakia","institution_ids":["https://openalex.org/I59655833"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046677063","display_name":"Beloslav Rie\u010dan","orcid":null},"institutions":[{"id":"https://openalex.org/I207624831","display_name":"Slovak Academy of Sciences","ror":"https://ror.org/03h7qq074","country_code":"SK","type":"government","lineage":["https://openalex.org/I207624831"]},{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]},{"id":"https://openalex.org/I59655833","display_name":"Matej Bel University","ror":"https://ror.org/016e5hy63","country_code":"SK","type":"education","lineage":["https://openalex.org/I59655833"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"Beloslav Rie\u010dan","raw_affiliation_strings":["Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovsk\u00e9ho 40, 974 01 Bansk\u00e1 Bystrica, Slovakia","Institute of Mathematics and Computer Science, Mathematical Institute Slovak Academy of Sciences, \u0160tef\u00e1nikova 49, 814 73 Bratislava, Slovakia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovsk\u00e9ho 40, 974 01 Bansk\u00e1 Bystrica, Slovakia","institution_ids":["https://openalex.org/I59655833"]},{"raw_affiliation_string":"Institute of Mathematics and Computer Science, Mathematical Institute Slovak Academy of Sciences, \u0160tef\u00e1nikova 49, 814 73 Bratislava, Slovakia","institution_ids":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064546889","display_name":"Anna Tirp\u00e1kov\u00e1","orcid":"https://orcid.org/0000-0002-4432-3528"},"institutions":[{"id":"https://openalex.org/I306340464","display_name":"Constantine the Philosopher University in Nitra","ror":"https://ror.org/038dnay05","country_code":"SK","type":"education","lineage":["https://openalex.org/I306340464"]}],"countries":["SK"],"is_corresponding":true,"raw_author_name":"Anna Tirp\u00e1kov\u00e1","raw_affiliation_strings":["Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, Tr. A. Hlinku 1, 949 74 Nitra, Slovakia"],"raw_orcid":"https://orcid.org/0000-0002-4432-3528","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, Tr. A. Hlinku 1, 949 74 Nitra, Slovakia","institution_ids":["https://openalex.org/I306340464"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5064546889"],"corresponding_institution_ids":["https://openalex.org/I306340464"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09860444,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"7","issue":"3","first_page":"59","last_page":"59"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.8689000010490417,"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"}},"topics":[{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.8689000010490417,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.8511000275611877,"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/real-number","display_name":"Real number","score":0.7457466125488281},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7258914113044739},{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.7046135067939758},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.574813187122345},{"id":"https://openalex.org/keywords/zermelo\u2013fraenkel-set-theory","display_name":"Zermelo\u2013Fraenkel set theory","score":0.527164876461029},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.48867443203926086},{"id":"https://openalex.org/keywords/number-theory","display_name":"Number theory","score":0.46528640389442444},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.4529132843017578},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4365704357624054},{"id":"https://openalex.org/keywords/urelement","display_name":"Urelement","score":0.41321098804473877},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3206453323364258},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.22689536213874817},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.1974245309829712}],"concepts":[{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.7457466125488281},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7258914113044739},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.7046135067939758},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.574813187122345},{"id":"https://openalex.org/C51460","wikidata":"https://www.wikidata.org/wiki/Q191849","display_name":"Zermelo\u2013Fraenkel set theory","level":5,"score":0.527164876461029},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.48867443203926086},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.46528640389442444},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.4529132843017578},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4365704357624054},{"id":"https://openalex.org/C78550038","wikidata":"https://www.wikidata.org/wiki/Q1896657","display_name":"Urelement","level":5,"score":0.41321098804473877},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3206453323364258},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.22689536213874817},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.1974245309829712},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms7030059","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms7030059","pdf_url":"https://www.mdpi.com/2075-1680/7/3/59/pdf?version=1534861653","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ba8178ad7197448a9777af1726271cfa","is_oa":true,"landing_page_url":"https://doaj.org/article/ba8178ad7197448a9777af1726271cfa","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 7, Iss 3, p 59 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/7/3/59/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms7030059","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms7030059","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms7030059","pdf_url":"https://www.mdpi.com/2075-1680/7/3/59/pdf?version=1534861653","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2888112425.pdf","grobid_xml":"https://content.openalex.org/works/W2888112425.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2395709426"],"related_works":["https://openalex.org/W2031083694","https://openalex.org/W1574825745","https://openalex.org/W288388583","https://openalex.org/W3034881686","https://openalex.org/W423103167","https://openalex.org/W2350176099","https://openalex.org/W2979076867","https://openalex.org/W4233243512","https://openalex.org/W2491940682","https://openalex.org/W102859336"],"abstract_inverted_index":{"In":[0],"the":[1,8,24],"present":[2],"paper":[3],"we":[4],"consider":[5],"one":[6],"of":[7,11,27],"basic":[9],"theorems":[10],"probability":[12],"theory":[13],"on":[14],"real":[15,28],"numbers.":[16,29],"We":[17],"prove":[18],"that":[19],"it":[20],"is":[21],"equivalent":[22],"with":[23],"supremum":[25],"axiom":[26]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
