What does nondecreasing mean?
Nondecreasing describes a quantity, sequence, or function that never gets smaller as its input or index moves in the relevant direction. It may rise, but it is also allowed to remain unchanged. Thus, a nondecreasing sequence can be 2, 2, 5, while a strictly increasing sequence cannot repeat a value. The term is especially common in mathematics, statistics, computer science, and economics, where separating “never decreases” from “always increases” matters. In everyday English, it is more technical than “doesn't go down” and is usually reserved for a defined sequence, function, measure, or trend. The word is useful because it captures a one-sided condition without implying strict growth: equal values are permitted, but decreases are not. This distinction underlies ideas involving sorted orders, monotonicity, cumulative totals, and algorithms that process data while allowing repeated values.
adjectiveIn mathematics and related technical contexts, a nondecreasing quantity or function never decreases as its input or index increases; it may remain constant or increase.
- Never decreasing; either constant or increasing at each successive step.
"The cumulative totals form a nondecreasing sequence, even when some daily gains are zero."
"The sorted list of prices is nondecreasing from the first entry to the last."
"A nondecreasing function preserves the order of any two inputs when they are compared."
Nondecreasing allows a plateau, but never a drop—equal values are fine, declines are not.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does nondecreasing come from?
The word is a modern English formation combining the Latin-derived prefix non-, meaning “not,” with decreasing. Decreasing comes from Latin decrescere, formed from de-, meaning “down” or “away,” and crescere, meaning “to grow.” Related forms such as increase, crescendo, and decrescendo ultimately share the same Latin root crescere.
How nondecreasing is actually used
This is a formal technical term used chiefly in mathematics, analysis, algorithms, statistics, and other quantitative fields. It is also used predicatively, as in “the sequence is nondecreasing.”
Easily confused with nondecreasing
A nondecreasing sequence may stay level or rise, whereas a nonincreasing sequence may stay level or fall.
In mathematical usage, increasing usually means strictly increasing, while nondecreasing permits consecutive equal values.