ickeminskande

The term ickeminskande is a Swedish linguistic construction that is used primarily in mathematical contexts to refer to a function or sequence that does not decrease as its independent variable increases. It is formed from the negation prefix icke, meaning “not,” and the adjective minskande, meaning “decreasing.” Thus, ickeminskande literally means “not decreasing,” which in English mathematical terminology is commonly translated as “non‑decreasing” or “weakly increasing.”

In a mathematical sense, a sequence \(a_n\) is ickeminskande if for all indices \(i\) and \(j\) with \(i < j\) one has \(a_i \leq a_j\). Similarly, a real‑valued function \(f\) defined on an interval is ickeminskande when \(x < y\) implies \(f(x) \leq f(y)\). The term appears in Swedish textbooks on calculus, algebra, and discrete mathematics, often to contrast with icke stigande (not increasing) or strictly increasing.

The concept is important in analysis because ickeminskande functions preserve order and have well‑defined limits at boundary points of their domains. In combinatorics and computer science, ickeminskande sequences often arise when counting objects in a way that the count cannot decrease when the size parameter grows.

In everyday Swedish usage outside mathematics, the word is rarely encountered. It most commonly appears in technical or academic writing on topics such as monotonicity, stability analysis, and algorithm analysis.