Absteigende

Absteigende is a German adjective derived from the prefix ab- (down, away) and the verb steigen (to rise). It denotes movement downward or a decrease in value, level, or magnitude. In technical usage, especially in mathematics and the sciences, it is used to describe things that decline as another variable increases or over time.

In mathematics, absteigende Folge means a sequence {a_n} with a_{n+1} ≤ a_n for all n; if the inequality is strict, one may say eine streng absteigende Folge. A decreasing function can be referred to as absteigende Funktion or, more commonly, as monoton fallend; speakers often use absteigend in expressions like absteigende Kurve depending on the noun.

Outside mathematics, the term appears in economics, physics, and geography to describe downward trends or slopes. For example, eine absteigende Nachfrage or eine absteigende Kurve can describe a curve that slopes downward, and eine absteigende Tendenz may refer to a general downward trend in data.

Grammatically, absteigende is the attributive form of the participle used before feminine or plural nouns in the nominative and accusative cases (e.g., eine absteigende Kurve). With masculine or neuter nouns, different endings are used (ein absteigender Trend, ein absteigendes Muster).

In sum, absteigende serves as a concise descriptor for phenomena that decrease, descend, or slope downward across various domains.