Negligible function

For a similar term, please see negligible set. (disambiguation)

In mathematics, a negligible function is a function ${\displaystyle \mu$ :\mathbb {N} \to \mathbb {R} } such that for every positive integer c there exists an integer N_c such that for all x > N_c,

${\displaystyle |\mu (x)|<{\frac {1}{x^{c}}}.}$

Equivalently, we may also use the following definition. A function ${\displaystyle \mu$ :\mathbb {N} \to \mathbb {R} } is negligible, if for every positive polynomial poly(·) there exists an integer N_poly > 0 such that for all x > N_poly

${\displaystyle |\mu (x)|<{\frac {1}{\operatorname {poly} (x)}}.}$