{"title":"Unified Proofs of Three Fundamental Properties of Continuous Functions","authors":"D. Daners","doi":"10.1080/0025570X.2022.2125725","DOIUrl":null,"url":null,"abstract":"Summary We provide a unified approach to three fundamental properties of continuous functions on closed and bounded intervals: the intermediate value theorem, and the uniform continuity theorem. We prove all three using the same building block, only making use of the least upper bound axiom and the definition of continuity.","PeriodicalId":18344,"journal":{"name":"Mathematics Magazine","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics Magazine","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/0025570X.2022.2125725","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
Summary We provide a unified approach to three fundamental properties of continuous functions on closed and bounded intervals: the intermediate value theorem, and the uniform continuity theorem. We prove all three using the same building block, only making use of the least upper bound axiom and the definition of continuity.
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