{"title":"A Rigorous Procedure for Generating a Well-ordered Set of Reals without use of Axiom of Choice/Well-ordering Theorem","authors":"Karan Doshi","doi":"10.9734/bpi/ctmcs/v9/3400","DOIUrl":"https://doi.org/10.9734/bpi/ctmcs/v9/3400","url":null,"abstract":"Well-ordering of the Reals@@ presents a major challenge in Set theory. Under the standard Zermelo Fraenkel Set theory (ZF) with the Axiom of Choice (ZFC), a well-ordering of the Reals is indeed possible. However the Axiom of Choice (AC) had to be introduced to the original ZF theory which is then shown equivalent to the well-ordering theorem. Despite the result however, no way has still been found of actually constructing a well-ordered Set of Reals. In this paper the author attempts to generate a well ordered Set of Reals without using the AC i.e. under ZF theory itself using the Axiom of the Power Set as the guiding principle.","PeriodicalId":420784,"journal":{"name":"Current Topics on Mathematics and Computer Science Vol. 9","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132169815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}