elementområde

Elementområde is a term used in some Scandinavian-language mathematical texts to refer to the set of elements associated with a particular object, most commonly the domain of a function. The exact meaning and preferred usage vary by country and author, and the term is not universally standardized in English-language mathematics.

In the standard mathematical sense, elementområdet (the domain) is the set of all inputs for which a function or relation is defined. If a function f maps from a set X to a set Y, then X is the elementområde of f. This set is distinct from the codomain (the target set Y) and from the image or range, which is the subset of Y consisting of actual outputs f(x) for x in X.

Examples help clarify the concept: if f: {1, 2, 3} → ℝ is defined by f(x) = x^2, the elementområde (domain) is {1, 2, 3}. The codomain is ℝ, and the image is {1, 4, 9}.

Usage notes: elementområde is not a universal or exclusively used term in all Scandinavian texts. Some authors prefer domän, definisjonsområde, or other equivalents. The exact terminology may differ by language and educational tradition.

Beyond functions, the idea of an elementområde can also appear in broader contexts as the underlying set of elements over which a relation, operation, or structure is defined, sometimes referred to as the carrier set or universe of discourse.

See also: domain, codomain, range, mapping, set. Etymology: from element (element) and område (area/region).