悖论对数学发展的影响

©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(1.,546300;2.,,547219)[][];;[]O144.2[]A[]1005-765(2003)04-0062-031,3:(1),();(2),();(3),,(),,,,,22.1500,,,,(),():,,,:RtABC,a=b,c2=2a2,ac,c,a,c=2m,(2m)2=2a2,a2=2m2,a,,,:,,,,,,,,,,,19,,,,2.126X[]2003-09-20[](1966-),(),,(1981-),,2001,©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(490430)(45,9),4(1)():AB,ABC,CACD,,,,,,(2):(),,,,(3):,,(4):ABC,,B,C,B(C),C(B)BC,4,,;,,4,,,(),,,,,,,,;,,,2.317,,,,y=xn:(x+x)n=xn+nxn-1x+[n(n+1)/2]xn-2(x)2++(x)nyxy/x=[(x+x)n-xn]/x=nxn-1+[n(n-1)/2]xn-2x++nx(x)n-2+(x)n-1,x,y=xnnxn-1,:x,x,x,x,?,x,191821,,,,,,,202.4301970,,,,,1902,:B,:BB?BB,BB,B,BB;,B²B,BB,36©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:!(),,!,,,,?,,,,(ZFC),,,,,,,,,,3,,,,,,,,,,,,,,,,:,,,,[1].[J].,2002,(5):42-43.[2].[J].,2001,(4):63-64.[3].[M].:,1980.[4].[M].:,1987.TheInfluencesofParadoxesontheDevelopmentofMathematicsHUANGYan2Ling1,DAIXian2jun2(1.DepartmantofMathematics,HechiCollege,Yizhou,Guangxi546300;2.YueliMiddleSchool,Nandan,Guangxi547219,China)[Abstract]Thispaperanalyzessomeimportantparadoxesinthemathematicsdevelopmentandshowsthatthecircularprocessofthegeneratingofaparadoxtheresolvingofitthegeneratingofanewoneistheprocessthatgivesmathematicthoughtsandmethodsgreatdevelopment.[Keywords]paradox;mathematiccrisis;settheory46