[分析] 是否是可數集

[elfkiller (沒有暱稱)]

一個有限集是可數集
令 S = { A : A 是有限集}
(也就是包含所有有限集的集合)
問:
是否有此集合的存在?
若有,試問是可數還是不可數?

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→ Sfly        :let T be any set. consider [T]:={{t}| t in T}.
→ Sfly        :if S is a set, then [T] is a subset of S
→ Sfly        :and card(S) >= card([T])=card(T)
→ Sfly        :then card(S) can be arbitrary large
→ Sfly        :which is contradicts with S is a set.
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