Re: [分析] 高微
※ 引述《jacky7987 (憶)》之銘言：
: 3.Let N={1,2,3,..} and E be defined as follow: A is contained in E iff A is
: a subset of N. Show that there is a bijective mapping from E to an open
: interval (0,1).
題目只是要證存在，所以不要真的去找阿
Let f: E -> (0,1),
f(A) := Σ 1/2^k.
k in A
但空集合和N要另外定，隨便挑個值就好了
很顯然這個函數onto但是不1-1
Let g: E -> (0,1),
f(A) := 1/10 + Σ 1/10^k.
k in A
而這函數1-1但不onto
根據某個定理你可以得到 #E=#(0,1).
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 111.250.110.175
推
09/16 16:44, , 1F
09/16 16:44, 1F
→
09/16 16:45, , 2F
09/16 16:45, 2F
→
09/16 16:50, , 3F
09/16 16:50, 3F
推
09/16 17:09, , 4F
09/16 17:09, 4F
→
09/16 18:16, , 5F
09/16 18:16, 5F
→
09/16 18:16, , 6F
09/16 18:16, 6F
→
09/16 18:17, , 7F
09/16 18:17, 7F
→
09/16 18:18, , 8F
09/16 18:18, 8F
→
09/16 18:19, , 9F
09/16 18:19, 9F
→
09/16 18:20, , 10F
09/16 18:20, 10F
→
09/16 18:20, , 11F
09/16 18:20, 11F
討論串 (同標題文章)