24小时热门版块排行榜    

北京石油化工学院2026年研究生招生接收调剂公告
查看: 718  |  回复: 4

yeyejingjing

新虫 (初入文坛)

[求助] show that the space of polynomials is not complete 已有1人参与

How to show that the space of polynomials is not complete. And the norm is defined by the maximum of the absolute value of the coefficient of polynomial.
For example, p(x)=\sum_{k=0}^n c_{k}x^{k}, ||p||=max_{k}|c_{k}|.

Help~!!!!
回复此楼

» 猜你喜欢

已阅   回复此楼   关注TA 给TA发消息 送TA红花 TA的回帖

junefi

铁杆木虫 (正式写手)

【答案】应助回帖

感谢参与,应助指数 +1
Consider a sequence of polynomials . We can see that is Cauchy (with respect to the above norm) but actually which is not in the space of polynomials.
理论改变世界!
2楼2015-10-28 15:11:39
已阅   回复此楼   关注TA 给TA发消息 送TA红花 TA的回帖

yeyejingjing

新虫 (初入文坛)

引用回帖:
2楼: Originally posted by junefi at 2015-10-28 15:11:39
Consider a sequence of polynomials \left\{ {{p_n};{p_n} = \sum\limits_{i = 0}^n {\frac{{{x^i}}}{{i!}}} } \right\}. We can see that \left\{ {{p_n}} \right\} is Cauchy (with respect to the above norm)  ...

这个不对吧,,如果是这个序列的话,,||pn||=max{1/i!}=1
3楼2015-10-28 15:18:05
已阅   回复此楼   关注TA 给TA发消息 送TA红花 TA的回帖

junefi

铁杆木虫 (正式写手)

【答案】应助回帖

★ ★ ★ ★ ★ ★ ★ ★ ★ ★
yeyejingjing(Edstrayer代发): 金币+10, good 2015-10-29 02:13:31
引用回帖:
3楼: Originally posted by yeyejingjing at 2015-10-28 15:18:05
这个不对吧,,如果是这个序列的话,,||pn||=max{1/i!}=1...

1, The definition of a complete metric space M: if every Cauchy sequence in M converges in M.
2, is Cauchy: for , .
3, is not in the space of polynomials.
理论改变世界!
4楼2015-10-28 15:28:20
已阅   回复此楼   关注TA 给TA发消息 送TA红花 TA的回帖

yeyejingjing

新虫 (初入文坛)

引用回帖:
4楼: Originally posted by junefi at 2015-10-28 15:28:20
1, The definition of a complete metric space M: if every Cauchy sequence in M converges in M.
2, \left\{ {{p_n}} \right\} is Cauchy: for n<m, \left\| {{p_n} - {p_m}} \right\| = \left\| {\sum\lim ...

嗯嗯,,,我也看明白了,,非常感谢啊
5楼2015-10-28 15:59:04
已阅   回复此楼   关注TA 给TA发消息 送TA红花 TA的回帖
相关版块跳转 我要订阅楼主 yeyejingjing 的主题更新
最具人气热帖推荐 [查看全部] 作者 回/看 最后发表
[考研] 一志愿哈尔滨工业大学材料与化工方向336分 +5 辰沐5211314 2026-03-26 5/250 2026-03-28 01:48 by 飞行日记西
[考研] 085600 286分 材料求调剂 +4 麻辣鱿鱼 2026-03-27 4/200 2026-03-28 00:50 by 无懈可击111
[考研] 277跪求调剂 +5 1915668 2026-03-27 8/400 2026-03-27 19:53 by WYUMater
[考研] 一志愿上海理工能源动力(085800)310分求调剂 +3 zhangmingc 2026-03-27 4/200 2026-03-27 19:01 by 给你你注意休息
[考研] 269专硕求调剂 +10 金恩贝 2026-03-21 10/500 2026-03-27 15:10 by caszguilin
[考研] 315调剂 +4 0860求调剂 2026-03-26 5/250 2026-03-27 11:23 by wangjy2002
[考研] 316求调剂 +5 江辞666 2026-03-26 5/250 2026-03-27 08:08 by hypershenger
[考研] 325求调剂 +5 李嘉图·S·路 2026-03-23 5/250 2026-03-27 00:42 by wxiongid
[考研] 0703化学求调剂 +3 丹青奶盖 2026-03-26 5/250 2026-03-26 20:11 by macy2011
[考研] 求调剂 +8 Auroracx 2026-03-22 8/400 2026-03-26 19:55 by 不吃魚的貓
[考研] 281求调剂 +6 Koxui 2026-03-24 7/350 2026-03-26 15:37 by 无际的草原
[考研] 0856求调剂 +8 zhn03 2026-03-25 9/450 2026-03-26 13:42 by zzll406
[考研] 寻找调剂 +5 倔强芒? 2026-03-21 8/400 2026-03-26 13:25 by 0906ljy
[考研] 调剂310 +3 温柔的晚安 2026-03-25 4/200 2026-03-25 23:16 by peike
[考研] 07化学303求调剂 +5 睿08 2026-03-25 5/250 2026-03-25 22:46 by 418490947
[考研] 生物学学硕求调剂 +7 小羊睡着了? 2026-03-23 10/500 2026-03-25 02:24 by 清风拂扬。 m
[考研] 环境学硕288求调剂 +8 皮皮皮123456 2026-03-22 8/400 2026-03-23 23:47 by 热情沙漠
[考研] 一志愿国科过程所081700,274求调剂 +3 三水研0水立方 2026-03-23 3/150 2026-03-23 23:11 by MajorWen
[考研] 336化工调剂 +4 王大坦1 2026-03-23 5/250 2026-03-23 18:32 by allen-yin
[考研] 一志愿南大,0703化学,分数336,求调剂 +3 收到VS 2026-03-21 3/150 2026-03-21 18:42 by 学员8dgXkO
信息提示
请填处理意见