What does nonnegative mean?
Nonnegative describes a number or quantity that is zero or greater than zero. It is an important distinction in mathematics because a positive number is strictly greater than zero, while a nonnegative number includes zero at its lower boundary. The term is especially common in arithmetic, algebra, analysis, probability, and computing. For example, a nonnegative integer may be zero or any positive integer, and a nonnegative matrix contains no entries below zero. The word is also frequently used in specifications, algorithms, and data validation to state that an input cannot fall below the baseline. Although “not negative” can express the same idea in less technical language, “nonnegative” is the standard precise term when zero must explicitly be included.
adjectiveDenoting a number or quantity that is greater than or equal to zero. In mathematics, a nonnegative value is either positive or zero and never negative.
- Greater than or equal to zero; not negative.
"The algorithm requires all input values to be nonnegative."
"Every nonnegative integer can be written as a sum of nonnegative squares."
"The software rejects any input that is not nonnegative."
Nonnegative numbers include the whole nonnegative side of the number line, from zero onward, making them indispensable in mathematics, computing, and statistics.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does nonnegative come from?
The word combines the prefix non-, meaning “not,” with negative, from Latin negativus, itself related to negare, “to deny” or “to say no.” The resulting term developed as a mathematical and scientific expression for values that are not below zero. Its related forms include negation and negate, which share the same Latin root.
Related word forms
How nonnegative is actually used
This is primarily a mathematical and technical term. It is commonly written without a hyphen, although “non-negative” is also accepted. In general prose, “zero or positive” may be easier to understand.
Easily confused with nonnegative
A positive number is strictly greater than zero, whereas a nonnegative number may be zero or greater than zero.