Surjektivt

Surjektivt is the Danish term used to describe a surjective or onto function in mathematics. A function f from a set A to a set B is surjektiv if every element of B is the image of at least one element of A; in symbols, for every y in B there exists x in A with f(x) = y. This requirement depends on the chosen codomain B, so changing B can change whether a given f is surjektiv.

Example: Let A = {1, 2, 3} and B = {a, b}. The mapping f(1) = a, f(2) = b, f(3) = b is surjektiv because both a and b have preimages in A. By contrast, the map g: {1, 2} → {a, b, c} with g(1) = a and g(2) = b is not surjektiv since c has no preimage.

Surjektivt is one of the standard classifications of functions, alongside injektiv (injective) and bijektiv (bijective). A surjektiv function maps A onto the entire codomain B, i.e., its image equals B. For finite sets, a surjectiv map from A to B requires |A| ≥ |B|; if |A| = |B| and f is surjektiv, then f is bijektiv. Surjective maps appear in many areas of mathematics, such as linear algebra and abstract algebra, where they describe how a structure maps onto another.