Alafunktsioon

Alafunktsioon is a term used in Estonian mathematical and computer science contexts to describe a supporting or auxiliary function that forms part of a larger construction. The word combines “ala-” (under, sub) with “funktsioon” (function), and its exact meaning can vary by field and author. It is not a universal standard across languages, but it is commonly understood as a function derived from or accompanying a main function.

In practice, an alafunktsioon may refer to several related ideas. It can denote a component function in a product-valued mapping, for example a function f: X → Y × Z whose projections pY∘f: X → Y and pZ∘f: X → Z are considered separate, or “subfunctions.” It can also mean a function obtained by restricting the domain or codomain of a larger function, i.e., a restriction or partial view of f. Additionally, alafunktsioon can be used for auxiliary or helper functions introduced to simplify proofs or algorithms.

Examples help illustrate the idea. If f: R → R×R is defined by f(x) = (x^2, sin x), then the two coordinate functions x ↦ x^2 and x ↦ sin x can be viewed as alafunktsioonid of f. If g is the restriction of f to a subset A ⊆ X, then g: A → Y is another form of an alafunktsioon relative to f.

Terminology notes: since usage varies, it is advisable to check the definition given in a specific text or course. Alafunktsioon is best understood as a broad label for auxiliary, derived, or restricted functions accompanying a main function. See also auxiliary function, projection, partial function, and restriction.