Allgemeinausdruck

Allgemeinausdruck is a German term used to denote a general expression that stands for a whole class of objects rather than a single instance. It arises from Allgemein (general) and Ausdruck (expression). In mathematics, logic, and related disciplines, such expressions are used to capture a family of forms by including variables or parameters that can be later instantiated.

In mathematics, a general expression encodes a family of objects. For example, the linear form ax + b is the general expression for any linear function of one variable, where a and b are parameters. The polynomial of degree n can be written as P(x) = a0 + a1 x + ... + an x^n; here the coefficients a0,...,an define the specific member of the family. The general equation of a conic, x^2 + y^2 + Dx + Ey + F = 0, similarly represents all circles and ellipses with appropriate parameter choices.

In logic and computer science, Allgemeinausdruck can refer to abstract schemes or templates, such as a universal quantification pattern (forall x, P(x)) or a lambda-like expression that, with substitutions, yields concrete instances. Such general expressions are useful for proving statements about entire classes, rather than checking individual cases.

Notes: The exact usage varies by field and author; the term is more common in didactic contexts than as a formal technical label. It typically emphasizes generality and the possibility of specialization through substitution, rather than presenting a fixed, concrete object.