# What is $n_0$ in the definition of neglibible? [duplicate]

Negligible Function: a function $$f(n)$$ is negligible if $$\forall$$ polyn. $$p \;\exists n_0 \text{ s.t. }\forall n>n_o\; f(n) < 1/p(n)$$
• What is exactly $$n_0$$? Why is there an $$n_0$$ in the definition?
• Why does not it suffice to say $$\forall n, f(n) < 1/p(n)$$ ?