funktio

Funktio is the Finnish term for function, a fundamental concept in mathematics and computer science. In its standard mathematical sense, a function f from a domain X to a codomain Y assigns to every element x in X exactly one element y in Y. This relationship is commonly denoted f: X → Y with f(x) = y. The set of outputs that actually occur is called the range, while the codomain is the target set Y and the domain is X.

Functions may be defined by a formula, a rule, a table, or an algorithm. They can be represented in multiple ways: as analytic expressions such as f(x) = x^2, as tabulated input-output pairs, or as procedures executed by a computer. In real and complex analysis, a function connects numbers to numbers or other objects; in discrete mathematics they map elements of finite or countable sets.

In programming, a function is a reusable block of code that produces an output for given inputs. Functions can be pure or impure, accept multiple parameters, and be composed with other functions. In many languages, functions are first-class citizens and can be passed as arguments, returned from other functions, or stored in data structures; higher-order functions are central to functional programming.

Etymology and usage: The word function comes from Latin functio, meaning performance or execution. The Finnish term funktio was adopted into scientific vocabulary during the 19th and 20th centuries to describe the same mathematical and computational idea.