negligible

Negligible is an adjective used to describe something of so little importance or quantity that it may be ignored in analysis or decision making. The word comes from the Latin neglegabilis, from neglegere, meaning “to neglect.” In common usage, one might say that the extra tax is negligible or that the difference between two results is negligible.

In mathematics, science, and engineering, negligible indicates a quantity whose effect is essentially zero within the context or precision of interest. It is often used to justify ignoring small terms or errors. For example, a rounding error smaller than the measurement precision may be described as negligible. In asymptotic analysis, a term f(n) is negligible relative to g(n) if the ratio f(n)/g(n) tends to zero as n grows, i.e., f = o(g).

Because negligibility is context dependent, a term considered negligible in one scenario may not be in another. Practically, scientists specify a tolerance or significance level to determine when a quantity can be treated as negligible. In probability, events with probabilities tending to zero may be treated as negligible for large samples, though care is needed in finite settings.

Common synonyms include insignificant, minor, or trivial, though each carries its own nuance. The concept appears across disciplines such as law, risk assessment, and economics when small effects are disregarded in modeling.