reellen

Reellen is the inflected form of the German adjective reell, used in mathematics to describe properties or objects related to real numbers. It is not a separate mathematical object; rather, it marks that the subject involves real numbers or real-valued quantities. The form reellen appears in phrases where the adjective modifies a plural noun in certain grammatical cases, such as mit reellen Zahlen (with real numbers), reellen Komponenten (real components), or ohne reellen Werte (without real values). The common noun phrase die reellen Zahlen denotes the set of real numbers.

In mathematical German, reell contrasts with terms referring to complex or imaginary quantities. For example, reelle Funktionen are real-valued functions, and reelle Zahlen describe elements of the real number system. The set of real numbers, often denoted by R, includes all rational and irrational numbers and serves as the foundation for real analysis and calculus.

The concept of real numbers can be introduced through various constructions, such as Dedekind cuts or Cauchy sequences, and is characterized by being an complete ordered field. Real numbers extend the rational numbers and provide a continuum suitable for measuring, graphs, limits, and continuity. The adjective reell, and by extension its inflected form reellen, thus functions primarily as a grammatical marker in German mathematics, signaling that a discussion concerns the real number system or real-valued objects.

See also: Real numbers; Real-valued functions.