mængden

Mängden is the definite form used in Swedish to denote “the set” in mathematics. In mathematical usage, a set is a collection of distinct objects, called elements, for which membership can be asserted or denied. Sets are typically denoted by listing their elements within curly brackets, for example, {1, 2, 3} or {a, b, c}. The symbol ∈ expresses “is an element of”; the empty set ∅ contains no elements.

Key concepts include subset relations, denoted by ⊆, where A ⊆ B means every element of A is also in B; equality of sets means mutual containment. Set operations include union A ∪ B, intersection A ∩ B, and difference A \ B. The complement A^c or A′ consists of all elements not in A with respect to a universal set U.

The power set P(A) is the set of all subsets of A. The cardinality |A| counts the elements; sets can be finite or infinite. Examples: the set of natural numbers N, the set of letters in the alphabet, or the set of prime numbers less than 10.

In logic and mathematics, the concept of a set is foundational, with axioms such as extensionality: two sets are equal if they have the same elements. Sets can be described by properties via set-builder notation, for instance {x ∈ N : x is even}.

The term mängden is used in Swedish-language texts to refer to a particular set being discussed, e.g., mängden {1, 2, 3} or mängden av primtal mindre än 10.