##  [Hausdorff Distance](/hausdorff-distance) 

  ##  [Hausdorff Distance](https://natural.quantumdictionary.io/hausdorff-distance-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A metric on the nonempty compact subsets of a metric space defined by the smallest epsilon such that each set is contained in the epsilon-neighborhood of the other; equivalently the maximum of the two directed set-to-set distances.

 

 

 

 

 





 

 



 ##  [Hausdorff Distance](https://puremath.quantumdictionary.io/hausdorff-distance-1) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A metric on the family of nonempty bounded subsets of a metric space defined as the maximum of the two directed suprema of distances from points of one set to the other (equivalently the infimal r such that each set is contained in the r-neighbourhood of the other).