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19946(80)()122(20),,:,:,,,,,,,,,,,,1,,1S(x},(i)Vx5.x(11)Va,xS,xaS2S{x},(i)VxS,x(11)V0x,S,x,)S3Sx},(i)VxS,ex(11)VA={yIVxS,xy},S4S~{x},(i)VxS,x(11){x}cs,x~(,:~oo)S{x,:}S,,x~n)N),S:994924,,,,;,,1,,S,,a,Sx,X21,a,,3,,,4,,1S(l)S=(xlxZ(2}(2)S~{yly51:ix,x(10,)}(3,S4,S{xIx,m,nN,m,n,,:m}(l).x,2,~xs,s:V0,(2),225.,x~2,2,.1.sups~.infs~(2)x(0,),o,inx11s,os.v,y,i,---,-J-2~S,yl,2sups=l,infs(3)illfs05,,sups~+oo,01,},(n),4infs;{}s,~1(,~co),4sups1---n+1/J,:+1~,,24,()S,S2A,B,(1)sup{AUB}=max{supA,supB};(2)inf{AUB}=min(infA,infB}.(l)M=max{supA,supB}M)supA)x(VxA)M)supB)x(VxB)M)x(VxAUB)infAinfB,m~infAVO,xA,xm+,xAUBminf{AUB},,(l)S,S{x}xS},infs-=sups,sups=infs(2)ST,tS,VSS,tT,supTinfs,,(l)(),()?(2)S(),S?(s)Ssupsinfs,S?,2:(),()-,,,,,,,:fC[a,,[a,,f(x):xa,,f(x),f(x),x,f,f(x)f(x),fc(a.b),x,,f(x)a,x,x(a,b),x,[x,x,,f(x)f(x),S{x}xxo,b,[xox,f(x)f(x)}sups~bS:xf[a,x(a,b),S={x.x[x,b,[xox,f(x)f(x)},S,sups~,~bS,sups~,{x,)S,x,(,:~),xS,[x,xf(x)=f(x)[x,,f)=f(x)..S,bb,b,f(~(x),f,f,b),(7,x),f(x)f(f(x),,x,f(x)-f(x),S,x.supsbx,::{a},,a,},,st,p{a,.}aa},V0,a{a},5.taa,{a},n)N,a,,)a,aa,,aa},aaaaa+,VO,N,nN,aaa+,lima=a:{a,b},,[a,b,n1,2.:S~:},,S,(a},ab(n1,2,){b,},a72b,(n=l,2,).!ba(,:N)..==[a.,,(n=l,2):{a}:VC,N,n,mN,la,}:,1,N,mN+1,N,},a}1,a,la,a,+1,},{a},-supa.}.4{x,:,}{x,:},5.tx:~(,:~co)..V0,N,m,,,,RN,}a,al:/2,la;]/2,:N,m=,,*RN,la.llaa*I}an*I/2+/2~..a}::s~{x},,SsuPS~,,4,{x}S,x~n~co)S,S:a,,H,,H,a,:H[a,,x[a,,[a,H,:Sx}x,b,[a,x}S,,S,sS~,b,[a,,(a,.a,a,xH,[a,H,S,~b,,b,b,b,xlS,S,,~bS,,[a,H,,:,S;,S();,,,,¹7S,;º,.,;»,,,ONTHETEACHINGOFSUPREMUMANDINFIMUMMaoXuhuaABSTRACTFirst,Givingfourequivalentdifinitionsofsupremum,thenanalyseexamples,thewriterbringtolightthemeaningofsupremumandthegeneralprineipleofapplyingsuprmum(infimum)PrineiPle.Keywords:suPremuminfimumstlpremum(infimum)Prineiple.