 ##  [Covering Number](/index.php/covering-number) 

  ##  [Covering Number](https://mathlogic.quantumdictionary.io/covering-number-0) 

  
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- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

The covering number N(ε,S,ρ) of a set S in a metric space (X,ρ) is the minimal number of closed balls of radius ε (with respect to ρ) whose union contains S; it quantifies how many small-radius “patches” are needed to cover S.