[閒聊] prove

看板MeganLai作者 (阿搞( ￣ c￣)y▅▅ξ)時間15年前 (2009/04/21 01:32), 編輯推噓76(76推 0噓 88→)
留言164則, 17人參與, 最新討論串1/1
A nondecreasing sequence which is bounded above converge to the least upper bound of its range pf:Let{an}n=1~infinite be the sequence as above so a1<=a2<=a3<=.... let S={an|1<=n<=infinite} and M=the least upper bound Then we are going to show lim an = M that for epsilon>0 exist k belong to N such that for all n>=k |an-M| <epsilon first since M is an upper bound for all n we have an<=M so for epsilon>0 we have an<M+ epsilon for all n belong to N On the other hand for epsilon >0 by them11.1.2 exist k belong to N such that M-epsilon<ak moreover sine{an} is a nondecreasing sequence M-e<ak<=an n>=k Hence for all n>=k M-e<an so for this epsilon >0 and thos h belong to N we have M-e<an<M+e n>=k Hence we have |an-M|<epsilon ----------------------------------------- Prouduct rule lim an = L , lim bn = M , lim an*bn=L*M pf: for all epsilon>0 exist k1 belong to N n>=k1 such that |an-L|<e/2(|M|-1) for all epsilon>0 exist k2 belont to N n>=k2 such that |an-L|<1 an<|L|+1 for all epsilon>0 exist k3 belong to N n>=k3 such that |bn-M|<e/2(|L|-1) take k=Max{k1,k2,k3} |anbn-LM|=|anbn-anM+anM-LM|<=|an||bn-M|+|M||an-L| <|L+1||bn-M|+|M+1||an-L|=e/2+e/2=e -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.114.218.19
推
04/21 01:33, , 1F
全英文的証明欸！ 菸小弟你不錯噢(拍)
04/21 01:33, 1F
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04/21 01:33, , 2F
XDD
04/21 01:33, 2F
推
04/21 01:34, , 3F
爽
04/21 01:34, 3F
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04/21 01:34, , 4F
32分 還是要水桶XD
04/21 01:34, 4F
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04/21 01:35, , 5F
不早說 我在推文那浪費了太多時間 不然應該來得及
04/21 01:35, 5F
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04/21 01:35, , 6F
老娘看到這個會不會以為走錯版
04/21 01:35, 6F
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04/21 01:35, , 7F
阿搞的證明我看不懂.... (畫圈)
04/21 01:35, 7F
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04/21 01:35, , 8F
XDDD
04/21 01:35, 8F
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04/21 01:37, , 9F
小菸是用背的嗎?
04/21 01:37, 9F
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04/21 01:37, , 10F
是的
04/21 01:37, 10F
推
04/21 01:37, , 11F
說真的 你背了出社會也用不到
04/21 01:37, 11F
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04/21 01:38, , 12F
被這個 只是為了應付考試= = 不然這個敘述很基本= =
04/21 01:38, 12F
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04/21 01:38, , 13F
可是要先應付考試..說不定小菸之後當老師
04/21 01:38, 13F
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04/21 01:38, , 14F
這樣就會用的到..。XD
04/21 01:38, 14F
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04/21 01:38, , 15F
拒絕當老師XDDD
04/21 01:38, 15F
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04/21 01:39, , 16F
我要給小菸一個章!!
04/21 01:39, 16F
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04/21 01:39, , 17F
不然海綿其實我們都可以不用上學阿..在家被爸媽教
04/21 01:39, 17F
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04/21 01:39, , 18F
這篇是天書
04/21 01:39, 18F
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04/21 01:39, , 19F
一加一等於二就夠用了這樣
04/21 01:39, 19F
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04/21 01:40, , 20F
XDD 有計算機就夠了這樣XDD
04/21 01:40, 20F
推
04/21 01:41, , 21F
XDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
04/21 01:41, 21F
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04/21 01:42, , 22F
黑呀..不過受教育應該還有更多東西要學，例:團體生活
04/21 01:42, 22F
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04/21 01:42, , 23F
EX:宅宿舍
04/21 01:42, 23F
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04/21 01:42, , 24F
小菸只考一題嗎?你應該要繼續在推文中默寫?!
04/21 01:42, 24F
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04/21 01:43, , 25F
= =
04/21 01:43, 25F
※ 編輯: winston628 來自: 140.114.218.19 (04/21 01:50)
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04/21 01:45, , 26F
XDDDDDDDDDDDDDDDDDDDDDDDD
04/21 01:45, 26F
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04/21 01:45, , 27F
XDDDDD 我是讓你享有推文的樂趣兼顧念書耶...讚!
04/21 01:45, 27F
推
04/21 01:52, , 28F
XD 優
04/21 01:52, 28F
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04/21 01:52, , 29F
老娘會不會有一天也把論文寫在這呢?(期待)
04/21 01:52, 29F
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04/21 01:53, , 30F
XDDD 釣魚文? 顆顆
04/21 01:53, 30F
※ 編輯: winston628 來自: 140.114.218.19 (04/21 01:56)
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04/21 01:58, , 31F
XDDDDDD 拋磚引玉這樣..。XD
04/21 01:58, 31F
推
04/21 02:03, , 32F
越來越多了耶XDD
04/21 02:03, 32F
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04/21 02:04, , 33F
一樣又是我看不懂的證明 (畫圈)
04/21 02:04, 33F
推
04/21 02:12, , 34F
包子我也看不懂(握)
04/21 02:12, 34F
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04/21 02:13, , 35F
等小菸考完再叫他解釋一下(翻成中文這樣)
04/21 02:13, 35F
推
04/21 02:13, , 36F
我也看不懂(握握)
04/21 02:13, 36F
推
04/21 02:15, , 37F
那我們看不懂得去旁邊坐一桌這樣 看會不會有第四咖
04/21 02:15, 37F
還有 87 則推文
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04/21 18:34, , 125F
他掛忙碌啊 水球也砸不醒XDDDDD
04/21 18:34, 125F
推
04/21 18:35, , 126F
是喔...哈哈哈哈
04/21 18:35, 126F
推
04/21 18:35, , 127F
海綿已經完全中仙劍毒這樣!好好喔~我要也玩啦!!
04/21 18:35, 127F
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04/21 18:36, , 128F
正取20名，備取8名
04/21 18:36, 128F
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04/21 18:36, , 129F
噗!打電話給他...XD
04/21 18:36, 129F
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04/21 18:36, , 130F
大家都來砸海綿水球~~讓她醒一下!XDDDD
04/21 18:36, 130F
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04/21 18:37, , 131F
水球應該沒用吧..
04/21 18:37, 131F
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04/21 18:37, , 132F
包子開晚點名啦!
04/21 18:37, 132F
推
04/21 18:39, , 133F
可是我不知道要喇啥~所以啦!月星你開~(推)
04/21 18:39, 133F
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04/21 18:39, , 134F
XDDDDDDDDD
04/21 18:39, 134F
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04/21 18:39, , 135F
阿搞笑什麼?(搔頭)
04/21 18:39, 135F
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04/21 18:40, , 136F
沒什麼 顆顆
04/21 18:40, 136F
推
04/21 18:40, , 137F
喇鴨舌這樣XDDD
04/21 18:40, 137F
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04/21 18:40, , 138F
說一下嘛...(推)
04/21 18:40, 138F
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04/21 18:42, , 139F
傻笑 顆顆
04/21 18:42, 139F
推
04/21 18:43, , 140F
米西卡咧?該不會在寫了吧?(歪頭)
04/21 18:43, 140F
推
04/21 18:44, , 141F
乾脆就直接這篇當點名文就好啦!等它爆了再開~(茶)
04/21 18:44, 141F
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04/21 18:44, , 142F
可能哦XDDD 這樣聊著聊著 這篇也快爆了XDD
04/21 18:44, 142F
推
04/21 18:47, , 143F
月底又到了 我又要開始大忙了這樣
04/21 18:47, 143F
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04/21 18:48, , 144F
月底又到了 我又要開始拮据了這樣
04/21 18:48, 144F
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04/21 18:54, , 145F
某郎 挖馬來造
04/21 18:54, 145F
推
04/21 18:56, , 146F
阿搞!!!(抓)
04/21 18:56, 146F
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04/21 18:57, , 147F
XDD 挖要來去忙了 估掰 晚點見
04/21 18:57, 147F
推
04/21 18:58, , 148F
我在吃午餐這樣XD
04/21 18:58, 148F
推
04/21 18:59, , 149F
阿搞晚點見阿!米西卡中午吃啥?(好奇貌)
04/21 18:59, 149F
推
04/21 19:07, , 150F
包子快點po晚點名啦..(推)我手上還有三份圖沒畫..= =
04/21 19:07, 150F
推
04/21 19:10, , 151F
冏爆 老娘連三天都有上來 都沒遇到這樣 XDDDD
04/21 19:10, 151F
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04/21 19:14, , 152F
我還沒下班@@
04/21 19:14, 152F
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04/21 19:16, , 153F
最好是找到新人~還越忙越晚這樣~
04/21 19:16, 153F
推
04/21 19:18, , 154F
好啦!我有PO了...請各位移駕吧~(茶)
04/21 19:18, 154F
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04/21 20:10, , 155F
包子 我午餐吃麥當當這樣......
04/21 20:10, 155F
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04/21 20:11, , 156F
俄國的麥當當好吃嗎??
04/21 20:11, 156F
推
04/21 20:12, , 157F
跟台灣一樣啊XDDDDD
04/21 20:12, 157F
推
04/21 20:13, , 158F
XDDDDDDDDDDDDDDDDD
04/21 20:13, 158F
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04/21 20:14, , 159F
聽說每一個國家都有特別的口味...原來是假的!
04/21 20:14, 159F
推
04/21 20:25, , 160F
喔 他最近出了墨西哥雞肉捲 結果裡面是麥香雞的雞肉
04/21 20:25, 160F
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04/21 20:26, , 161F
不是很好吃這樣....
04/21 20:26, 161F
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04/21 23:40, , 162F
麥香雞的雞肉 (冏)XDDD
04/21 23:40, 162F
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04/21 23:57, , 163F
按進來這篇真的有走錯版的FU XDDDD
04/21 23:57, 163F
推
04/22 00:06, , 164F
XDDDDDDDDDDDDDDDDDDDDDDD 麥香雞的雞肉 XDDDDDDDDDD
04/22 00:06, 164F
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文章代碼(AID): #19xB6NNd (MeganLai)