Negligible Function

Definition

A function $f:\mathbb{N}\to \mathbb{R}$, $f\in negl(\lambda )$ if:

• $\forall c\in {\mathbb{Z}}_{>0}$,
• ${\lim }_{\lambda \to \infty }f(\lambda )\ast {\lambda }^c=0$

Alternate Definition

The function $\mu :\mathbb{N}\to \mathbb{R}$ defined such that $\forall c\in {\mathbb{Z}}^{>0}$ s.t $\exists N_c\in \mathbb{Z}$ s.t $\forall x>N_c$, $|\mu (x)|<\frac{1}{x^c}$