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1、Instructor’sSolutionsManualtoaccompanyANALYSISwithanIntroductiontoProof5thEditionStevenR.LayLeeUniversity≤Copyright2014PearsonEducation,IncUpperSaddleRiver,NewJersey07458Copyright©2014PearsonEducation,Inc.2Thismanualisintendedtoaccompanythe5thedition
2、ofAnalysiswithanIntroductiontoProofbyStevenR.Lay(Pearson,2013).Itcontainssolutionstonearlyeveryexerciseinthetext.Thoseexercisesthathavehints(oranswers)inthebackofthebookarenumberedinboldprint,andthehintsareincludedhereforreference.Whilemanyoftheproof
3、shavebeengiveninfulldetail,someofthemoreroutineproofsareonlyoutlines.Forsomeoftheproblems,otherapproachesmaybeequallyacceptable.Thisisparticularlytrueforthoseproblemsrequestingacounterexample.Ihavenottriedtobeexhaustiveindiscussingeachexercise,butrat
4、hertobesuggestive.Letmeremindyouthatthestarredexercisesarenotnecessarilythemoredifficultones.Theyaretheexercisesthatareusedinsomewayinsubsequentsections.Thereisatableonpage3thatindicateswherestarredexercisesareusedlater.Thefollowingnotationsareusedth
5、roughoutthismanual:8=thesetofnaturalnumbers{1,2,3,4,…};=thesetofrationalnumbers<=thesetofrealnumbers"=“forevery”$=“thereexists”§=“suchthat”Ihavetriedtobeaccurateinthepreparationofthismanual.Undoubtedly,however,somemistakeswillinadvertentlyslipby.Iwo
6、uldappreciatehavinganyerrorsinthismanualorthetextbroughttomyattention.StevenR.Layslay@leeuniversity.eduCopyright©2014PearsonEducation,Inc.3TableofStarredExercisesNote:TheprefixPindicatesapracticeproblem,theprefixEindicatesanexample,theprefixTrefersto
7、atheoremorcorollary,andtheabsenceofaprefixbeforeanumberindicatesanexercise.StarredStarredExerciseLaterUseExerciseLateruse2.1.26T3.4.114.3.144.4.52.2.102.4.264.4.108.2.142.3.322.5.34.4.168.3.93.1.3E7.1.74.4.17T8.3.33.1.47.1.75.1.146.2.83.1.6E8.1.15.1.
8、16T6.2.93.1.74.3.10,4.3.15,E8.1.7,T9.2.95.1.185.2.14,5.3.153.1.8P8.1.35.1.195.2.173.1.244.1.7f,E5.3.75.2.10T7.2.83.1.273.3.145.2.117.2.9b3.1.30b3.3.11,E4.1.11,4.3.145.2.13T5.3.5,T6.1.7,7.1.133.2.6a4.1.9a,T4.2.1,6.2.23,7.2.16,T9.2.95.2.169.2.153.2.6bT
