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1、•howtwoex-studentsturnedontopuremathematicsandfoundtotalhappinessamathematicalnovelettebyD.E.KnuthSURREALNUMBERS./+,ADDISONWESLEYThisbookhasbeentypesetwith'fEX,inComputerModernwithAlbertuschapterheadings.ThecoverandillustrationsweredesignedbyJillC.Knuth.Internetpagehttp:I/www-cs-faculty.s
2、tanford.edurknuth/sn.htmlcontainscurrentinformationaboutthisbookandrelatedbooks.Copyright©1974byAddison-WesleyPublishingCompany,Inc.Phillippinescopyright1974byAddison-WesleyPublishingCompany,Inc.Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitte
3、d,inanyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,withoutthepriorwrittenpermissionofthepublisher.PrintedintheUnitedStatesofAmerica.PublishedsimultaneouslyinCanada.LibraryofCongressCatalogCardNo.74-5998.ISBN0-201-03812-9171819BKMBKM09876Seventeenthprinting,Ap
4、ril2006CONTENTSTheRock12Symbols83Proofs144BadNumbers195Progress276TheThirdDay347Discovery418Addition489TheAnswer5510Theorems6311TheProposal7112Disaster7613Recovery8214TheUniverse8915Infinity9716Multiplication106Postscript..1131THEROCK,...�-...........,,....c!lf.��'�..../'..����..---·-··
5、A.Bill,doyouthinkyou'vefoundyourself?B.What?A.Imean-hereweareontheedgeoftheIndianOcean,milesawayfromcivilization.It'sbeenmonthssinceweranofftoavoidgettingsweptupinthesystem,and"tofindourselves."I'mjustwonderingifyouthinkwe'vedoneit.3B.Actually,Alice,I'vebeenthinkingaboutthesamething.These
6、pastmonthstogetherhavebeenreallygreat-we'recompletelyfree,weknoweachother,andwefeellikerealpeopleagaininsteadoflikemachines.ButlatelyI'mafraidI'vebeenmissingsomeofthethingswe've"escaped"from.Youknow,I'vegotthisfantasticcravingforabooktoread-anybook,evenatextbook,evenamathtextbook.Itsounds
7、crazy,butI'vebeenlyingherewishingIhadacrosswordpuzzletoworkon.A.Oh,c'mon,notacrosswordpuzzle;that'swhatyourparentsliketodo.ButIknowwhatyoumean,weneedsomementalstimulation.It'skindaliketheendofsummervacationswhenwewerekids.InMayeveryyearwecouldn'twaittogetoutofschool
