Funktionsnachweis

Funktionsnachweis is a German term that denotes the demonstration or proof that a function has a certain property or that a proposed function behaves as specified. It is used in mathematics, computer science and engineering, and can also refer to evidence that a system or component performs its intended function in practice.

In mathematics, a Funktionsnachweis concerns proofs about functions, such as existence, well-definedness, and properties like continuity, differentiability, monotonicity, integrability or bijectivity. Typical proof methods include direct construction, epsilon-delta arguments for continuity or limits, proof by contradiction, and proof by induction. In constructive contexts, a Funktionsnachweis may also yield an algorithm that computes function values.

In applied fields, the term describes verification that a function or subsystem meets specified requirements. This encompasses functional testing, simulations, and, where relevant, formal verification. The goal is to ensure that the function performs correctly under defined conditions and constraints, and to document compliance with standards and safety or quality requirements.

Overall, Funktionsnachweis connects theoretical justification with practical assurance: it formalizes that a function meets its intended criteria, whether in abstract mathematics or in real-world systems. See also proof of correctness, functional testing and formal verification.