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1、Limits,LimitsEverywherePhotooftheauthorstandinginfrontofRichardDedekind’shouseinBraunschweig(July2010)©TijanaLevajkovicLimits,LimitsEverywhereTheToolsofMathematicalAnalysisDAVIDAPPLEBAUM33GreatClarendonStreet,OxfordOX26DPOxfordUniversityPressisadepartmentoftheUniversityofOxford.Itfurtherst
2、heUniversity’sobjectiveofexcellenceinresearch,scholarship,andeducationbypublishingworldwideinOxfordNewYorkAucklandCapeTownDaresSalaamHongKongKarachiKualaLumpurMadridMelbourneMexicoCityNairobiNewDelhiShanghaiTaipeiTorontoWithofficesinArgentinaAustriaBrazilChileCzechRepublicFranceGreeceGuatem
3、alaHungaryItalyJapanPolandPortugalSingaporeSouthKoreaSwitzerlandThailandTurkeyUkraineVietnamOxfordisaregisteredtrademarkofOxfordUniversityPressintheUKandincertainothercountriesPublishedintheUnitedStatesbyOxfordUniversityPressInc.,NewYork©DavidApplebaum2012Themoralrightsoftheauthorhavebeena
4、ssertedDatabaserightOxfordUniversityPress(maker)Firstpublished2012Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,withoutthepriorpermissioninwritingofOxfordUniversityPress,orasexpresslypermittedbylaw,orundertermsagreedwi
5、ththeappropriatereprographicsrightsorganization.EnquiriesconcerningreproductionoutsidethescopeoftheaboveshouldbesenttotheRightsDepartment,OxfordUniversityPress,attheaddressaboveYoumustnotcirculatethisbookinanyotherbindingorcoverandyoumustimposethissameconditiononanyacquirerBritishLibraryCa
6、taloguinginPublicationDataDataavailableLibraryofCongressCataloginginPublicationDataLibraryofCongressControlNumber:2011945216TypesetbyCenveoPublisherServicesPrintedinGreatBritainonacid-freepaperbyClaysLtd,StIvesplcISBN978-0-19-964008-913579108642ToBenandKate‘thecool.’Strongstuff,isn’tit?Hep
7、aused.Limits,limitseverywhere.WilliamBoyd,TheNewConfessionsIntroductionhisbookiswrittenforanyonewhohasaninterestinmathematics.ItoccupiesTterritorythatliesmidwaybetweenapopularsciencebookandatraditionaltextbook.Itssubjectmatteristhepartofmathematicsthatiscalled
