##  [Profinite Completion](/profinite-completion) 

  ##  [Profinite Completion](https://mathlogic.quantumdictionary.io/profinite-completion-0) 

  

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- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The inverse limit (pro-object) of all finite quotients of a discrete group, ring, or other algebraic object, endowed with the inverse-limit topology; the result is a profinite (compact, totally disconnected, Hausdorff) topological object encoding the arithmetic of finite quotients.