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1、thefoundationsofmathematicsTHEFOUNDATIONSOFMATHEMATICSSecondEditionianstewartanddavidtall33GreatClarendonStreet,Oxford,ox26dp,UnitedKingdomOxfordUniversityPressisadepartmentoftheUniversityofOxford.ItfurtherstheUniversitysobjectiveofexcellenceinresearch,scholarship,andeducationbypublishingworldwide.
2、OxfordisaregisteredtrademarkofOxfordUniversityPressintheUKandincertainothercountries©JoatEnterprisesandDavidTall2015ThemoralrightsoftheauthorshavebeenassertedFirstEditionpublishedin1977SecondEditionpublishedin2015Impression:1Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrieva
3、lsystem,ortransmitted,inanyformorbyanymeans,withoutthepriorpermissioninwritingofOxfordUniversityPress,orasexpresslypermittedbylaw,bylicenceorundertermsagreedwiththeappropriatereprographicsrightsorganization.EnquiriesconcerningreproductionoutsidethescopeoftheaboveshouldbesenttotheRightsDepartment,Ox
4、fordUniversityPress,attheaddressaboveYoumustnotcirculatethisworkinanyotherformandyoumustimposethissameconditiononanyacquirerPublishedintheUnitedStatesofAmericabyOxfordUniversityPress198MadisonAvenue,NewYork,NY10016,UnitedStatesofAmericaBritishLibraryCataloguinginPublicationDataDataavailableLibraryo
5、fCongressControlNumber:2014946122ISBN9780198706441(hbk.)ISBN9780198706434(pbk.)PrintedandboundbyCPIGroup(UK)Ltd,Croydon,CR04YYLinkstothirdpartywebsitesareprovidedbyOxfordingoodfaithandforinformationonly.Oxforddisclaimsanyresponsibilityforthematerialscontainedinanythirdpartywebsitereferencedinthiswo
6、rk.TOPROFESSORRICHARDSKEMPwhosetheoriesonthelearningofmathematicshavebeenaconstantsourceofinspirationPREFACETOTHESECONDEDITIONheworldhasmovedonsincethefirsteditionofthisbookwaswrittenTontypewritersin1976.Forastart,thedefaultuseofmalepronounsisquiterightlyfrownedupon.Educationally,researchhasrevealed
7、newinsightsintohowindividualslearntothinkmathematicallyastheybuildontheirpreviousexperience(see[3]).1Wehaveusedtheseinsightstoaddcommentsthatencouragethereadertoreflectontheirownunderstanding,therebymakingmo
