Dedekind, Richard- Essays on the Theory of Numbers 1963

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1、$1.50ESSAYSONTHETHEORYOFNUMBERSContinuityandIrrationalNumbersTheNatureandMeaningofNumbersRICHARDDEDEKINDlESSAYSONTHETHEORYOFNUMBERSI.CONTINUITYANDIRRATIONALNUMBERSII.THENATUREANDMEANINGOFNUMBERSBYRICHARDDEDEKINDAUTHORIZEDTRANSLATIONBYWOOSTERWOODRUFFBEMANLATEPROFESSOROFMATHEMATICSTHEUNIVERS

2、ITYOFMICHIGANDOVERPUBLICATIONS,INC.NEWYORKThisnewDoveredition,firstpublishedin1963,isanunabridgedandunalteredrepublicationoftheEnglishtranslationfirstpublishedbyTheOpenCourtPublishingCompanyin1901.LibraryofCongressCatalogCardNumber:63-3681ManufacturedintheUnitedStatesofAmericaDoverPublicat

3、ions,Inc.180VarickStreetNewYork14,N.Y.CONTENTSI.CONTINUITYANDIRRATIONALNUMBERS.PAGEPreface1I.PropertiesofRationalNumbers3II.ComparisonoftheRationalNumberswiththePointsofaStraightLine.6III.ContinuityoftheStraightLine8IV.CreationofIrrationalNumbers12V.ContinuityoftheDomainofRealNumbers19VI.O

4、perationswithRealNumbers21VII.InfinitesimalAnalysis24II.THENATUREANDMEANINGOFNUMBERS.Prefaces31I.SystemsofElements44II.TransformationofaSystem50III.SimilarityofaTransformation.SimilarSystems53IV.TransformationofaSysteminItself56V.TheFiniteandInfinite.63VI.SimplyInfiniteSystems.SeriesofNatu

5、ralNumbers.67VII.GreaterandLessNumbers.VIII.FiniteandInfinitePartsoftheNumber-Series.81IX.DefinitionofaTransformationoftheNumber·SeriesbyInduction.83X.TheClassofSimplyInfiniteSystems92XI.AdditionofNumbers.96XII.MultiplicationofNumbers.101XIII.InvolutionofNumbers.104XIV.NumberoftheElementso

6、faFiniteSystemlOSCONTINUITYANDIRRATIONALNUMBERSCONTINUITYANDIRRATIONALNUMBERS.MYattentionwasfirstdirectedtowardtheconsid-erationswhichformthesubjectofthispam•phletintheautumnof1858.AsprofessorinthePolytechnicSchoolinZurichIfoundmyselfforthefirsttimeobligedtolectureupontheelementsofthediffe

7、rentialcalculusandfeltmorekeenlythaneverbeforethelackofareallyscientificfoundationforarithmetic.Indiscussingthenotionoftheapproachofavariablemagnitudetoafixedlimitingvalue,andespeciallyinprovingthetheoremthateverymagnitudewhichgrowscontinually,butnotbeyondalll