Boundedness

Boundedness refers to the property that a set or function stays within certain limits and does not grow infinitely large or small. In mathematics, a set is bounded if there is a finite boundary beyond which its elements do not go. Similarly, a function is bounded if its values stay within a fixed range, no matter what inputs are used. This concept helps describe stability and predictability, indicating that something remains controlled and does not become unmanageably large or small. Boundedness is fundamental in analysis, ensuring that certain behaviors or quantities are confined within manageable bounds.