nonnegligible

Nonnegligible is an adjective used to describe something whose effect, size, or probability is not small enough to be ignored. In mathematical and scientific contexts, a nonnegligible term or quantity cannot be omitted from analysis or modeling without potentially altering results; a negligible term is one that can be ignored within a specified tolerance or precision. The term is inherently contextual: what is nonnegligible in one model may be neglected in another with a looser tolerance or in a different regime.

Etymology and spelling notes: nonnegligible is formed from the prefix non- and the adjective negligible. English usage often prefers non- or nonnegligible; many writers also employ the hyphenated form non-negligible to improve readability. Both spellings are commonly understood, though hyphenation is still recommended by some style guides to reduce ambiguity.

Common contexts: in asymptotic analysis, a term is negligible if it tends to zero in a limit, whereas a nonnegligible term remains of nonvanishing magnitude in that limit. In probability, an event with nonnegligible probability has a lower bound away from zero as the sample size grows. In engineering and physics, nonnegligible effects must be included in models to ensure accuracy or safety, whereas truly negligible effects can be omitted without materially affecting outcomes.

See also: negligible, significance, asymptotic analysis, practical significance. The term remains inherently subjective, reflecting the chosen context, tolerance, and required precision of the analysis.