Little-o notation, written as $$\littleo{g(n)}$$, is a stronger statement than Big O notation. It implies that $$g(x)$$ grows much faster than $$f(x)$$. It’s defined as:

$f(x) = \littleo{g(x)} \overset{\Delta}{=} \lim_{x \to \infty} \frac{f(x)}{g(x)} = 0$

## Relationship with Big-O notation#

\begin{align}3n^3 &= \bigo{n^3} \\ 3n^3 &\ne \littleo{n^3} \\ 3n^3 &= \littleo{n^4}\end{align}

To use an analogy:

\begin{align}f(n) &\in \bigo{g(n)} &\implies f(n) &\le g(n) \\ f(n) &\in \littleo{g(n)} &\implies f(n) &< g(n)\end{align}