 ##  [Boundedness](/boundedness) 

  ##  [Boundedness](https://puremath.quantumdictionary.io/boundedness-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 &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

Property of a function, operator, or set that its values or elements have uniformly finite norm: a set S in a normed space is bounded if sup_{x∈S}‖x‖&lt;∞; a function f is bounded if sup_{x in domain}‖f(x)‖&lt;∞.