※ 引述《q0300768 (NANA真好看~^^)》之銘言：
: 交92(V)
: (a) Let a and b be real numbers with a<b, suppose that the function
: f:(a,b) → R is bounded and is monotonic increasing. Prove that
: both lim f(x) and lim f(x) exist, and so f can be extended to a
: x→a+ x→b-
: continuous function on [a,b].
Since f is bounded,c=sup{f(x)|a<x<b} and d=inf{f(x)|a<x<b} are finite.
Let ε>0. There exists B,a<B<b, s.t. c-ε<f(B)≦c.
If B<x<b,then c-ε<f(B)<f(x)≦c => |f(x)-c|<ε.
Thus,lim f(x)=c.
x→b-
Similarly, we have lim f(x)=d.
x→a+
--
http://0rz.tw/b42r6
禮奈：你看到了吧？
K1：沒...沒有啊，我什麼都不知道，哈哈(抓頭
禮奈：是這樣啊~
禮奈：http://0rz.tw/ef2uo
蟬：唧唧唧唧唧唧唧唧唧唧......
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 202.132.188.137