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