##  [Strong Convergence](/strong-convergence) 

  ##  [Strong Convergence](https://puremath.quantumdictionary.io/strong-convergence-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A mode of convergence in a normed linear space whereby a sequence (x_n) converges strongly to x if the norm of their difference tends to zero: ||x_n - x|| → 0. Strong convergence is equivalently called convergence in norm and is strictly stronger than weak convergence in infinite-dimensional spaces.