begrenset

Begrenset is a Dutch adjective meaning limited or bounded. It is used in everyday language to describe restrictions or a finite scope, for example when a budget, time frame, or set of possibilities is begrensd. In formal contexts, the term often signals that there is a definable boundary or constraint.

Etymology and related terms: Begrenset derives from be- (a prefix indicating cause or transformation) combined with grens (border or boundary) and the suffix -et. It is related to the noun begrenzing (limitation) and the verb begrenzen (to bound or limit). The word appears across many domains to convey that something is not unlimited.

In mathematics: Begrensd is used to describe a property of sets or sequences. A real-valued set S is begrensd if there exists a real number M such that for every x in S, the magnitude |x| ≤ M. This corresponds to the standard concept of boundedness in analysis. If no such M exists, the set is onbegrensd (unbounded). Boundedness is a common prerequisite for results involving convergence, compactness, and continuity.

In other domains: The term also occurs in legal, economic, and computer science texts to denote restrictions or finite limits. Examples include begrensde aansprakelijkheid (limited liability) and begrensde resources (limited or restricted resources). The phrase is used to indicate constraints that affect planning, modeling, or decision-making.

Translations: In English, begrenset translates as bounded or limited, depending on context. In mathematics it aligns with bounded; in general usage it more often conveys a practical restriction or finite extent.