1、5 4 1 995 M6 2 ;JO U R N AL OF JllA N U N IV ER SIT Y vol. 5 N o19 9 5L !.M ( “)K1MwZE L ! N b1oM (/) ; ; uW*K s $,7Q L ! K $, L !V Y ,C S N |+Z T , Bi5,; N, V V Mw, L ! M 8ZEbBY L ! 5:51 ( i )d b (/) “,A (/) b52 ( ) A l 0 b53 ( )L K“ B b54 ( ) AKb55 (K ) !qa , br B uW, Hqa , brB 7,5HAiK 7 uW, , br
2、B 7b56 (C a u e hy l 5)I, im xbi. ib o , N N , , n N H,!+B+! xA Ei O/, i , ! in fEbn5 i: o ,( cBb, a Eb) =a , k,b i/E ca , 0 Kb51 533j51 54+51 5551 56r !a , BC a u ehy ,5a . , i , != su p a , ,5 a NmKb51b 571 2r2 52 w B 552= 1 !Ed b , M B , |xb E ,wxo , Mr=sZE,/ a , , 561 2r52 57qr !(qa , ,xB uW*, ,
3、 ! c , , b, B l 0 K,a , , c qa , , b ,r(n = l , 2 ,l)3 53 w B 553 51mqr !Ed b , i ,/c, oc , a , E , b , E , i , ! cb , ) ,50E b53= 5 r53 54B5 8Br !ab,5 i , a , B xob l#ja . Vxoa ,Kb53 55qxQE.L ! , K ,/ alblqa=, bbr K, i , !lbb sY c,J, i K ZEw b53 56j !abBC au ehy , i , !a . N + 1 ab,5aba , Kb53b 57J
4、 !wab, b,rB uW*,5 i , !a , , b , sYi c,J,5 cB, O c qa . ,r(,B1 , 2 ,l)4 54 w B 554 51r 52w 51 ZE,/ a , , b, , ab E , f E , Oab, b, , # l a sEb54 52q54 53r 54w 52 , n5 B A0 b!E k“,5t AT H, Es T 0“,V7i O,y7 l , ! l xo ,5+E b54 55qrQE 52w 55 ZE/ *a , , fqa , ,j K, Oab,b , , w b54 56qr !a , BCau ch y ,
5、n5 54w 52 , abi0 , O,!abx ,N H |b 531 2r55 54qrQE. , ix qa , b , x a , K,5 ix a ,oB PU(m, =cK,T 7 uW“U= ,r(x, K w b55= 56rQEb!aa , BC a u ehy Oa , a , br, a= l ,5 ix qa , b , x qa . , 3 a l ,=, P (x ,=)ca , Kb/ 7 uW“U (x ,Y) ,K w b55 576 56 w B 556 5r56 52 !x= , x , qa , br, a , br=sZE,/ a , , b , ,
6、a , , bprcx , k,a , , C a u e hy , Olim a , = lim b , =y, /ZE Vx , B l c0 b56a 53q 56w 52ZEs c,5 aE b56 54qr !x , 9 O M ,5 in N , x l+M ,wx , , Mr=sZE/ ab, bb, a= + , b , x , ,C a u ehy5, ab , b , l , Olim a , = lim b , c, c= lim x ,b56 55q3QEb , K,a , =sZE/ a=bb ,qa , , K, acocCau ch y ,V7 l OB kB
7、c, 5ow55ZEw b56 57r !qa , , bbrB uW*,5ac , pcC a u c hy ,V7 l O kaBbcB c,a , , , in N , ( cb7 57 w B 557 51m57 52mB60B57 , 53lr57b 5457 55lr57 56l IDl =Sv “I. s.=,2ICI. s. S/, 19843qvI. s. , 19784 r. s. 2 , 198157KI. sT l. =Sv, 19846 .I. sl., 1987PR O O F E A C H O T H E R O F B A SICT H E O R E M O
8、 N R E A L N U M B E RPR O PE R T IE S O F CO MPL E T ESu n S hu r o n g(D e Pa r tm e n t o f Ma the m a tie s )A bstr a Cttheo r em by d ir e e tK ey w o rd sIn this p a p e r w e g iv e e q u iv ale n t p r o o f o n r e a l n u m be r p r o p e r ties o f e o m ple tPr o o f ea e h o the r .Su p re m u m a n d in fim u m , po in t o f a ee u m la tio n , eo v e rin g , N e s te d in te r v a lB61B
