mengden

Mengden is the definite form of a noun used in several Scandinavian languages, notably Danish and Norwegian. It can refer to a quantity or a collection of items in everyday language, and it is also the term used for a set in mathematical or formal contexts.

In Danish and Norwegian, the word exists in a base form (mængde in Danish, mengde in Norwegian) and takes a definite form (mængden in Danish, mengden in Norwegian) when the reference is specific. The same word thus covers both practical notions of amount and the more formal notion of a set or collection that consists of multiple elements.

In mathematics and logic, mengde is commonly used to denote a set: a well-defined collection of distinct objects. For example, the set of natural numbers can be described as a mengde, or mengden of tall, depending on the language and context. In everyday language, it is used to express quantities, such as the amount of data, people, or material: the mengde of data, the mengden av mennesker, the mengde salt required.

The term belongs to the Germanic language family and has cognates across Danish and Norwegian; the exact spelling varies by language and orthographic tradition. The distinction between its quantitative sense and its set-theoretic sense is primarily a matter of context, with mathematical usage requiring precision about which objects are included.

See also: Set (mathematics); Quantity; Scandinavian language terminology.