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(),2008,30(S2):456460CN53-1045/NISSN0258-7971JournalofYunnanUniversityΞ,(,650091):,,.:;;;;ZFC:G642.0;O143:A:0258-7971(2008)S2-0456-05,,:.:[12],[34],,[58],.:2,,,,[916].,?,?,,.1,400,.;,.,.,(,,;,,,),.,()..,?,2:.ZFC,ZFC,,.,,,:.,Ξ(Z533);()(YB)(65),,,,,:2008-11-10:07102008027.:19-.,ZF.ZF():;;;;;;;;.(AC).ZFACZFC.ZFC,ZFC,,ZFC,ZFC,.ZFC,ZFC,ZFC,,().,,(,,).:.,..,,.,,.,(),,.,.2,,.,.3:,:1(1)A,f(x)x0.Π0,0,0|x-x0|,|f(x)-A|,Af(x)xx0,limxx0f(x)=A.(2)limxx0f(x)=0,f(x)xx0.(3)X0,0,0|x-x0|,|f(x)|X,f(x)xx0,limxx0f(x)=.,,.1x0,f(x)x0.:(1)limxx0f(x)=,limxx01f(x)=0.(2)limxx0f(x)=0,x0f(x)0,limxx01f(x)=.1:,,,:.2A,B2.f:AB,AB1-1.B,B,,754S2:A1-1A...,A,B,AB,ABB0,ABBA,.3A.AAB,A.4A.AN,A();A().2.,,:xx0(),f(x)()(f(x)(),():X(),xx0:|x-x0|),.,(),.2,2.:{2n}+n=1,{2n}+n=1,,{2n}+n=1n,{2n}+n=1n();f(x)=1x,x[-1,0)(0,1],f(x),,f(x)x0().2,,.,,,,,.,,,2,.3,.,?,(),.,,?,(),,.,:limxx0f(x)=0,Π0,0,0|x-x0|,|f(x)|.:0,0,0|x-x0|,|f(x)|;0,0,0|x-x0|,|f(x)|;Π0,Π0,0,0|x-x0|,|f(x)|,[1115],,(,,854()300..,).,.2:ZFC.,ZFC,.,,.4,.,?,,ZFC,,,,.,.:2:,;,,,.2,,2,.,,2,.,,,,..,,,,.,ZFC,.,ZFC,,.,ZFC.,,,,,.,().,,.,.,,,(,),,,,,.,,,3,,954S2:..:.,.[1],,,.()[M].2.:,2003.[2].()[M].3.:,1995.[3],.[M].:,1979.[4],.()[M].:,1983.[5].[M].3.:,2002.[6].[M].:,1985.[7].[M].:,1989.[8].[M].:,2001.[9].[J].,2004,22(4):1202122.[10].[J].,2005,26(6):20222.[11].[J].:,2006,6(2):527.[12].()[J].,2006,27(6):29234.[13].()[J].,2007,28(3):33236.[14].()[J].,2007,28(6):16221.[15],.[J].,2003,19(5):11216.[16].[J].,2007,23(6):125.TheinfiniteviewsoftheuniversitymathematicsYANGZong2wen,LIYou2bao(DepartmentofMathematics,YunnanUniversity,Kunming650091,China)Abstract:Learningandunderstandingtotheinfiniteviewsofinmathematicsareanalyzed,letuniversitymathematicseducationhelptosetupthescientificmathematicalinfiniteviewsofinmathematicsoftheuniver2sitystudentsandtoimprovetheuniversitystudentsmathematicqualifications.Keywords:theinfinitelylargequantity;theinfinitelysmallquantity;theactualinfinite;thepotentialin2finite;theZFCaxiomaticsettheory064()30