推 unknow12:原來是我忽略了for all m,n >N 04/03 00:11
※ 引述《unknow12 (LockOn)》之銘言:
: 根據定義sequence(Xn)is Cauchy Sequence if every ε>0
: there is a nature number N , such that |Xm-Xn|<ε for all m,n>=N
: 那Xn=log(n)
: 有|X(n+1)-Xn|=log((1+n)/n)→0 as n→∞
: 滿足cauchy的條件阿
: 為什麼答案不是cauchy
令ε= 1/2 log 2
如果 Xn 是 Cauchy sequence
there is a nature number N , such that |Xm-Xn|<ε for all m,n>=N
是對的,
取 m=2n
則 | Xm -Xn|=log 2 > ε ...
--
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 71.63.157.14