推 goodGG :直接證 f(x') = 0 就好了.. 01/16 02:01
→ goodGG :用有理數列 x_n 去逼近 x'. 01/16 02:02
→ goodGG :因為 f: continuous, 所以 ... 01/16 02:02
→ yueayase :所以,我可以想辦法,用有理數列,去逼近一個無理數? 01/16 02:14
推 craig100 :e就是由有理數逼出來的無理數吧 01/16 02:22
看到這個敘述,我想到我看到得一題極限證明題:
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].
嘗試去做證明:
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?
到底該怎麼取?
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