作者yueayase (scrya)
看板Math
标题Re: [微积] 极限 & 连续
时间Sun Jan 16 01:53:42 2011
看到这个叙述,我想到我看到得一题极限证明题:
Let f be continous on [a,b] and let f(x) = 0 when x is rational.
Prove that f(x) = 0 for every x in [a,b].
尝试去做证明:
Proof:
Assume there is a irrational number x' in [a,b] such that f(x') = a ≠ 0
Then, we want to show that lim f(x) = 0 ?
x->x'
or want to show that f is not continuous?
到底该怎麽取?
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1F：推 goodGG :直接证 f(x') = 0 就好了.. 01/16 02:01
2F：→ goodGG :用有理数列 x_n 去逼近 x'. 01/16 02:02
3F：→ goodGG :因为 f: continuous, 所以 ... 01/16 02:02
4F：→ yueayase :所以,我可以想办法,用有理数列,去逼近一个无理数? 01/16 02:14
5F：推 craig100 :e就是由有理数逼出来的无理数吧 01/16 02:22