Definition:O Notation

Given two functions $$f \ $$ and $$g \ $$, the statement

$$f = O (g) \ $$

is equivalent to the statement

$$\exists \alpha>0 : \lim_{x \to \infty} \frac{f(x)}{g(x)} = \alpha \ $$.

The statement

$$f = o(g) \ $$

is equivalent to the statement

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

These are called big "oh" and little "oh", respectively.