Surjektva

Surjektva is a term used in mathematics, specifically in set theory and abstract algebra, to describe a type of function or mapping between two sets. A function f from a set A to a set B is called surjektva, or surjective, if every element in the codomain B has at least one element in the domain A that maps to it. In simpler terms, the function "hits" every possible output value in the codomain.

Formally, a function f: A -> B is surjective if for every element y in B, there exists at least one element x in A such that f(x) = y. This means that the image of the function, which is the set of all output values f(x) for x in A, is equal to the entire codomain B. If the image of the function is a proper subset of the codomain, meaning there are elements in B that are not produced by any element in A, then the function is not surjective.

Surjectivity is a fundamental property of functions and is often considered alongside injectivity (where each element in the codomain is mapped to by at most one element in the domain) and bijectivity (where a function is both injective and surjective). Understanding surjectivity is crucial for comprehending concepts like inverse functions, isomorphisms in algebra, and the construction of various mathematical structures.