##  [Cauchy Sequence](/cauchy-sequence) 

  ##  [Cauchy Sequence](https://natural.quantumdictionary.io/cauchy-sequence-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A sequence (x_n) in a metric space (X,d) is a Cauchy sequence if for every ε>0 there exists N such that for all m,n≥N one has d(x_m,x_n)<ε; terms become arbitrarily mutually close as the index grows.