Funksioner

Funksioner are mappings from a domain X to a codomain Y that assign each input x in X exactly one output y in Y, written as f(x). The domain X specifies allowable inputs, the codomain Y specifies potential outputs, and the image or range is the set { f(x) : x ∈ X }.

Key properties include injective (one-to-one), surjective (onto), and bijective (one-to-one and onto). Composition is defined by (g ∘ f)(x) = g(f(x)). The inverse exists if a funksion is bijective, allowing a reverse mapping. A funksion can be represented by formulas, tables, or graphs.

In mathematics and logic, funksioner underpin many concepts such as transformations, limits, and continuity. They are defined for diverse domains, from real numbers to vectors and more abstract sets, and can be extended to relations, depending on the formal framework.

In computer science, funksioner are fundamental building blocks of software. They take inputs (parameters), return outputs, and may be called with different arguments. Functions support modularity, abstraction, and reuse. Some are pure (no side effects), while others are impure and may alter external state. Higher-order funksioner can take other funksioner as arguments or return them; closures capture surrounding context.

Historically, the concept of funksioner matured through work of mathematicians such as Euler and Cauchy in the 18th–19th centuries and was later formalized in computer science in the 20th century.