Auswahlmenge

Auswahlmenge is a German term that translates literally to "selection set" or "choice set". In mathematics it refers to a subset chosen from a larger set that satisfies certain criteria. The concept is fundamental in set theory, combinatorics, and probability theory where one often works with a collection of all possible selections that meet specified conditions.

In combinatorial contexts, an Auswahlmenge can represent the set of all k-element subsets of an n-element set, often denoted as binomial coefficients. For example, the Auswahlmenge of all 3-member committees drawn from a 10-person group consists of \(\binom{10}{3}=120\) distinct subsets. Similarly, in probability theory the outcome space of a random experiment is an Auswahlmenge of all possible results. The probability of an event is then the ratio of the cardinality of the event's Auswahlmenge to that of the entire sample space.

In computer science, the term is used when a program selects a subset of data from a larger database according to specified filters; this subset is the Auswahlmenge. Graph theory also employs Auswahlmenge to refer to sets of vertices or edges satisfying particular properties, such as independent sets or dominating sets.

The definition of an Auswahlmenge is context‑dependent; it always denotes a set that is explicitly chosen or derived according to a defined rule. Understanding its role in different mathematical and applied disciplines is essential for precise communication and accurate problem solving.