nedadstigende

Nedadstigende is an adjective used in Danish and Norwegian to describe something that decreases in value as its index or input increases, or that slopes downward. The term literally translates as "downward-ascending" from ned- (down) and stigende (rising). In mathematical and scientific contexts it conveys a monotone direction that is not an increase. Related terms include stigende for increasing and synkende or faldende for decreasing, though usage varies by language.

In mathematics, nedadstigende describes monotone behavior. For a sequence a_n, nedadstigende means a_{n+1} ≤ a_n for all n. If all inequalities are strict, the sequence is strictly nedadstigende. For a function f defined on an interval, f is nedadstigende if x1 < x2 implies f(x1) ≥ f(x2).

Examples help illustrate the concept. The sequence 5, 3, 3, 1 is nedadstigende; the sequence 5, 4, 2, 2 is non-increasing. The function f(x) = 100 − x on any interval is nedadstigende. If the inequality is always strict, as in 5, 4, 3, 1, the sequence is strictly nedadstigende.

Usage notes: The term is common in Danish and Norwegian mathematical writing to describe a non-increasing trend. Depending on style, it may be used interchangeably with synkende or fallende, or with nedadgående in some contexts. In English-language texts, translations such as non-increasing or decreasing are typically used.