已知 A是个有限集, f : A →A 是单射,然后它也必须是满射,反过来也是。
问如果它是无限集的话还成立吗 不成立的话给个反例。
1 The members of the U.N. Peace Committee must choose, from among themselves, a presiding officer of
their committee. For each member x, let f(x) designate that member’s choice for officer. If no two
members vote alike, what is the range of f?
2 Let A be a finite set. Explain why any injective function f : A → A is necessarily surjective. (Look at
part 1.)
3 If A is a finite set, explain why any surjective function f : A → A is necessarily injective.
4 Are the statements in parts 2 and 3 true when A is an infinite set? If not, give a counterexample.
原题是4 说如果23是对的如何如何, 1应该没什么用。
高数单射满射的问题
答案:2 悬赏:40 手机版
解决时间 2021-04-03 17:36
- 提问者网友:留有余香
- 2021-04-03 09:22
最佳答案
- 五星知识达人网友:鱼芗
- 2021-04-03 09:45
无限集不成立,如R到R的映射y=arctanx,是单射但是不满
全部回答
- 1楼网友:行雁书
- 2021-04-03 09:51
满射的定义!!!你搞反了。是b中每个元素在a中都由至少一个原项与之对应,这道题,显然实数集r中存在,找不到原项的数啊。
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