##  [Triangle Inequality](/triangle-inequality) 

  ##  [Triangle Inequality](https://puremath.quantumdictionary.io/triangle-inequality-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A metric-space statement that for any three points x, y, z the distance from x to z does not exceed the sum of the distances from x to y and from y to z; symbolically d(x,z) ≤ d(x,y)+d(y,z).