[高微] 幾題題目！

[steve10042 (see11)]

都是是非題

1.__ If the sequence {an^2} converges, then the sequence {an} also converges.



2.__ Suppose that the sequence {an} is monotone and that it has a convergent

   subsequent subsequence. Then {an} converges.

3.__Every continuous function f:(0,1)→R has a bounded image.


4.___Suppose that the function f:[0,1]→R is continuous and its image is con-

   tained in set of rational numbers. Then f is a constant function.

麻煩了，如果有錯的可以說出是錯在哪嗎？

謝謝

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◆ From: 140.119.134.47
→ jacky7987   :1.  {a_n}={(-1)^n} div. but {a_n^2}=1 conv.
→ cgkm        :題目都沒有錯誤  請安心解題
→ forloricever:2 用夾擠, 3 考慮 1/x
→ FANggot     :4 可考慮intermediate value theorem
→ steve10042  :第一題我看懂了。可是後面的還不會耶
推 jacky7987   :第四題可以用connected set in R 只有空集合 單點和
→ jacky7987   :區間做好像也可以