[微積] 證明 Bolzano-Weierstass
Prove Bolzano-Weierstass Theorem
(Every bounded sequence has a convergent sequence.)
on the compact interval I=[0,1]
Using the following method:
Suppose, for a sequence {Sn}, there is no cluster point in I.
Then, around each point, there is an epsilon neighborhood
excluding all other points in the sequence.
Why does this lead to a contradiction?
Draw a diagram of the situation.
好讀圖片:http://ppt.cc/bMPA
麻煩大家幫我解這題! 請看圖片比較容易懂
老師已經先做第一步，
但是接下去的我還是不會做...
已經糾結了好幾個小時還是弄不懂該從何下手，光是老師的第一步就已經不太明白了
拜託大家幫幫我，謝謝!
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