What does nonincreasing mean?
Nonincreasing describes a quantity that never rises. In mathematical usage, it means that each value in a sequence, or each successive output of a function, is no greater than the preceding one; equal values are allowed, so a nonincreasing sequence may remain flat for a time, fall, or do both. This differs from strictly decreasing, which requires every successive value to be smaller, and it also differs from simply decreasing in some authors' terminology. The word is formal and is especially common in analysis, order theory, economics, and descriptions of trends. Outside technical writing, “not increasing” or “never rising” may sound more natural. Knowing the distinction matters because a plateau does not break monotonicity in the nonincreasing direction: the data may go down and stay level, but they may never go up. The prefix non- is therefore not merely casual shorthand; it specifies a precise mathematical relationship.
adjectiveNever increasing; specifically, in mathematics, remaining constant or decreasing at each successive step.
- Not increasing; in mathematics, equal to or less than the preceding value at each step.
"The sequence of monthly sales was nonincreasing, with each value no higher than the one before it."
"The sequence of monthly sales was nonincreasing, with each value no higher than the one before it."
"As the battery drained, its measured output remained nonincreasing, although the rate of decline was not constant."
The twist: nonincreasing does not forbid flat spots—it forbids upward steps.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does nonincreasing come from?
Nonincreasing was formed in English using the productive prefix non- and the present participle increasing. The latter comes from increase, borrowed from Latin increscere, meaning “to grow” or “to increase.” Its relatives include increment and the musical term crescendo, while crescent also ultimately reflects the Latin root crescere, “to grow.”
How nonincreasing is actually used
This is primarily a formal and technical term, especially common in mathematics, economics, and analysis. In ordinary writing, “not increasing” or “never rising” is usually clearer. Its mathematical sense permits equal successive values.
Easily confused with nonincreasing
A nonincreasing sequence never rises, whereas a nondecreasing sequence never falls; both may contain equal consecutive values.
In strict mathematical terminology, decreasing requires every successive value to be lower, while nonincreasing also allows values to remain equal.