##  [Modulus of Continuity](/modulus-continuity) 

  ##  [Modulus of Continuity](https://mathlogic.quantumdictionary.io/modulus-continuity-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A function ω:[0,∞)→[0,∞) with ω(0)=0 and typically nondecreasing such that |f(x)−f(y)| ≤ ω(|x−y|) for all x,y; it quantifies how function variation is controlled by input increments.

 

 

 

 

 





 

 



 ##  [Modulus of Continuity](https://puremath.quantumdictionary.io/modulus-continuity-1) 

  

 [![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 function ω: [0,∞) → [0,∞) that assigns to each scale δ the supremum of |f(x)-f(y)| over all pairs with distance at most δ; it quantifies the maximal oscillation of f at that scale.