Mindestwert

Mindestwert is a German term that denotes the smallest value that a variable, a set of values, or a function can take within a given context. The word is used across disciplines such as mathematics, statistics, economics, and data analysis to refer to the notion of a lower bound or minimum.

In mathematics, the minimum of a set S is an element m in S such that m ≤ s for every s in S. If such an element exists, S has a minimum or least element. A set may have no minimum, but still possess an infimum (greatest lower bound), which need not belong to the set itself. The concepts of lower bound, infimum, and minimum are related but distinct.

When applied to a function, the minimum value is the smallest value that the function attains over a specified domain. A function can have a global (or absolute) minimum on its domain, or a local minimum at points where the function value is smaller than at neighboring points. Under appropriate conditions, such as continuity on a compact domain, a continuous function is guaranteed to achieve its minimum.

In data analysis and measurement, the Mindestwert often refers to the smallest observed value in a data set or sample, sometimes used for quality checks or as a constraint in optimization problems. The term can be used synonymously with minimum, lower bound, or untere Grenze, depending on the context.