If f : X→Y is a one-to-one and onto function, and Y is a proper subset of X, which of the following statement is correct?
(a) X must be countably infinite
(b) Y must be countably infinite
(c) X must be infinite
(d) The cardinality of X is lager than Y
(e) None of the above
答案是c
想請問這題在考什麼概念呢?為什麼答案是c?完全沒有頭緒…
感謝!
3 則留言:
proper set是真子集
就是不會相等
所以如果是有限集因為1-1且onto所以基數相等
與真子集矛盾
所以必為無限集
但未必保證是可數集
懂了!
謝謝!
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