今天是:2024年11月25日 星期一
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1.4.12 Uniqueness of Limits
正文

  Theorem 2:The limit of a convergent sequence is unique.

  Proof bycontradiction : logarithmic sequence , if

,

Then according to the definition of limit , for any given , there exists such that

  When , there is always ;

  When , there is always .

  Taking , then for any given

,

When  exists , such that

So . This contradicts the hypothesis, so the original conclusion is correct. Certification completed.

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