Little o notation ($f=o(g)$)

When $g$ is nonzero sufficiently near the specified limit, little o notation meansThus the numerator becomes negligible relative to the denominator's scale. As $n\to \infty$, $n=o(n^2)$ because $n/n^2=1/n\to 0$; as $h\to 0$, $h^2=o(h)$ because $h^2/h=h\to 0$. The direction of the limit changes the comparison. ^[ref]

Equivalently, for every $\epsilon >0$, the bound $|f|\le \epsilon |g|$ holds sufficiently near that limit, with a threshold allowed to depend on $\epsilon$. Big O notation needs only one fixed multiplier, making it weaker. For example, $2n=O(n)$ but $2n$ is not $o(n)$. The useful relation $f\sim g⟺f-g=o(g)$ turns asymptotic equivalence into a statement about a negligible remainder.