作者suzzdicon (舒兹迪控)
看板Math
标题[微积] 连续性
时间Wed Oct 19 02:53:32 2011
Let f:[1,2]->Ｒ be the function given by
c
0 ,if x in [1,2]^Ｑ
f(x)={
1/n ,if x in [1,2]^Ｑ and x=m/n
m,n are natural numbers , f(1)=1
(1)
Prove that if ε>0 ,then the set {x in [1,2]:f(x)>ε}
has only a finite number of points.
(2)
Prove that f:[1,2]->Ｒ is continuous at each irrational number in [1,2]
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◆ From: 140.113.25.222
※ 编辑: suzzdicon 来自: 140.113.25.222 (10/19 02:54)
1F：推 plover :f is not well-defined. m & n are relative prime? 10/19 14:33