monotoneisesti

Monotoneisesti is a Finnish adverb meaning "monotonically" or "in a monotone manner." It is used primarily in mathematics, statistics, and related fields to describe nondecreasing or nonincreasing behavior of a quantity as another variable changes.

In mathematics, monotoneisesti describes how a function or sequence behaves with respect to its argument. A function f defined on a domain D is monotonisesti kasvava (monotonically increasing) if, for all x and y in D, x ≤ y implies f(x) ≤ f(y). It is monotonisesti laskeva (monotonically decreasing) if x ≤ y implies f(x) ≥ f(y). If the implication is strict (x < y implies f(x) < f(y)), the function is strictly monotone. The same idea applies to sequences: a sequence {a_n} is monotonisesti kasvava if a_n ≤ a_{n+1} for every n, and monotonisesti laskeva if a_n ≥ a_{n+1} for every n.

In practice, monotoneisesti is used to describe trends and relationships, such as a monotonically increasing growth curve, or a dataset that never decreases as the independent variable increases. Finnish texts may also use the related adjective monotoninen to describe the property itself, with monotoneisesti serving as the adverbial form.

See also: Monotone function, Monotonicity.