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1、e是无理数的证明方法(Eisaproofofirrationalnumbers)-----------------------1页-----------------------又又一期开封教育学院学报九年第一一明关于是无理的又证方法数桑震军刘月桂〔〕一函函摘要本文利用元数微积分中乘积数求导数的莱布尼兹公式和定积分的分,。部积分法证明是无理数,下利用反证法可证明是无理数现证明如??!,二,#、?正假设是有理数可令粤这里为数%??正和、?(与二)?下四况?用反证法假定有整数使则有边种情百、,,尹峨?率&???当车时!?牛&,??,山弓匀习#一当+时%?一一?和,?半??当,时,当
2、?&?,?时现在分别来讨论&?()斗%)水。,?%一)二+“十”,Atthistimetherewasthistype,evenontheleftandoddontheright,。Yes,%Thereisnocontradictionbetweennumbers()()%),When0,thereis?%two+1,2+two)"&"#+3"ten+2"-##(??,(&Oddnumbersatthistimeonly2,thatis,%two,/two..''.?2Theoddnumberontherightholdstheequation&+(%)/#),Whenthe
3、reisApricot32Two+2#?%two&42(2#?45#)."%%,4?,4,#),car,%62,Eventhen,theleftismultiples,butthe54iscontradictory"#/,,.,/0two72+282%sideedge#?/.Atthispointtheleftisright,andtherightiscontradictory4)&(%)//??#)+#'death?,,At99,thereisanevennumberontheleftandanoddnumberontheright。。Contradiction,butto
4、remove%/?7,thereisindeed,.Two.?2.%,%,/%:2,Two/3:Zheng/;//Tosumup,onlyifthereisnointegeradditionStand。Onelogic,onedifficulty,toone,Themethodofprooftoabsurdityisakindofdeductivemethodwhichisfamiliartomanypeople,andmanyproblemsaredifficulttoprove.One,live,cleverItiseasytosolvetheproblembyusing
5、thereductiontoabsurditymethod,butthereductiontoabsurditymethodisalsoahighskillinmathematicalproof,Next,Amethodtobewellfamiliarwithitstillneedsalotofeffort<2One-to-onePageand2-----------------------?Becauseofthelimit!&&.,One001?A?!??corpse?2+sheep?,Obviously,theremustbeoneThere'sacertainwayt
6、omakeitFourTo?/?,Soil.Three>one,flytwo1.,.",,,?",2,&5(&5(two,twoGuHanplaya22AstuffyLet&/&+(2male,young,,,,????/?Totheholepotentialtwoknives,alphabeta,Yi,femalebamboo,,?Β7)......事实上由菜布尼兹公式可得一5···?5一,/#,1一一,/“()Β&(&52(〔&?(“二&(二命/一2&,/5一)?一,(,2卫)/((&〔户吐十十…)#工二里&,。(5一?(〔&2一,(22〕&?(#…#匆生二)业主夕兰上卫
7、?/2Χ”、“5(......&)(五Δ气?一,??、>>>,,,>1>>,、油、,、>八、小二、,小,、,小一,和5(9、Ε、”夕甲,盖”Β、夕,?7一Γ”书熟阴丁水汀鳅?,“丁飘丁/,州状位石人Φ9>、、、、、、、、、/>>。二、,>及(9、,、。,,,山,2口盖”少,>八?222书二Γ一朋刁一、2一入声刁凡于隽又一刁西蕊?、?月扎八?22,男马Η一?“25”,?2一。”/,?2一一/·1、”,与一(〕?仅有〔”一(〕',9,故由和Ι(式知,5(&?(5与&(&?(的值必为整数?··4Κ”(Λ整积分