##  [Limit Superior](/limit-superior) 

  ##  [Limit Superior](https://puremath.quantumdictionary.io/limit-superior-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

For a sequence (a_n) of extended real numbers, the limit superior, denoted lim sup a_n, is lim_{n→∞} (sup_{k≥n} a_k). It equals the greatest subsequential limit and describes the largest accumulation behavior of the sequence as the index tends to infinity.