Untergrenze

Untergrenze is the German term for the lower bound or lower limit of a quantity. It designates a value that the quantity is not allowed to fall below or that serves as a threshold in measurement, regulation, or decision rules. The concept is used across mathematics, statistics, engineering, economics, and data analysis.

In mathematics, a real number L is a lower bound (Untergrenze) of a subset S of real numbers if L ≤ x for all x in S. The greatest lower bound, also called the infimum, is the largest of all such lower bounds. If the infimum belongs to the set, it may coincide with the minimum value. For example, for S = (0, 1), every L ≤ 0 is a lower bound; the infimum is 0, but S does not contain 0, so S has no minimum.

Beyond pure math, Untergrenze appears in applied contexts as a price floor in economics and finance (Preisuntergrenze), a lower specification limit in quality control, or a lower detection limit in measurement systems. These usages describe a threshold below which values are considered unacceptable, invalid, or outside a defined range.

Relation to other terms: the counterpart is Obergrenze (upper bound), and related concepts include limits, infimum, and minimum. While Untergrenze and Untere Grenze are sometimes used interchangeably in everyday language, precise mathematical writing often prefers Untere Schranke or infimum to avoid ambiguity.

In summary, the Untergrenze is a fundamental threshold indicating how low a quantity may reasonably be allowed to fall, with formal definitions in mathematics and practical applications in science, engineering, and economics.