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内有定义,证明:若对任何数列,极限都存在,则所有这些极限都相等。

问答题
2022-04-02 14:12
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正确答案
证明:任意,,由题知,都存在,设,,考虑数列:

,得收敛。作为的两个子列,也是相同的极限,有归结原则得,
的值都相等,且为任取的两极限为的数列。

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