2、ddurability.LibraryofCongressCataloging-in-PublicationDataLavine,Shaughan.Understandingtheinfinite/ShaughanLavine.p.em.Includesbibliographicalreferencesandindex.ISBN0-674-92096-1(alk.paper)I.Mathematics-Philosophy.l.Title.QA8.4.L381994511.3'22-dc2093-49697CIPPrefaceInwritingthisbookIhav
3、etriedtokeepmathematicalprerequisitestoaminimum.ThereaderwhoisessentiallyinnocentofmathematicalknowledgebeyondthattaughtinhighschoolshouldbeabletoreadatleasthalfwaythroughChapterVIIIpluspartsoftherestofthebook,thoughsuchareaderwillneedtoskiptheoccasionalformula.Thatisenoughofthebookfora
4、llofthemajorideastobepresented.TheIntroductionmayseemdauntingsinceitreferstoideasthatarenotexplaineduntillater-trustme,theyareexplained.Areaderwholearnedfreshmancalculusonce,butperhapsdoesnotrememberitverywell,andwhohashadalogiccoursethatincludedaproofofthecompletenesstheoremwillbeinfin
5、eshapethroughoutthebook,exceptforvarious"technicalremarks,"anappendixtoChapterVI,andafewpartsofChapterIX.Thosefewtechnicaldiscussionsrequirevaryingdegreesofmathematicalsophisticationandknowledgeofgeneralmathematicallogicplusoccasionalknowledgeofelementaryrecursiontheory,modeltheory,ormo
6、dallogic.ThanksaredueBonnieKent,VannMcGee,SidneyMorgenbesser,andSarahStebbinsfortheirinfinitepatienceinlisteningtomymanyhalf-bakedideasandfortheirsubstantialhelpincullingandcompletingthemwhileIwaswritingthisbook.Astheylearned,Icannotthinkwithoutthegiveandtakeofconversation.ThanksalsotoT
7、i-GraceAtkinson,JeffBarrett,WilliamBoos,HartryField,AlanGabbey,HaimGaifman,AlexanderGeorge,AllenHazen,GregoryLandini,PenelopeMaddy,RobertMiller,EdwardNelson,AhmetOmurtag,DavidOwen,CharlesParsons,ThomasPogge,VincentRenzi,ScottShapiro,MarkSteiner,andRobertVaughtfortheirthoughtful
