<Dl> <Dd> f (x) = O (g (x)) as x → ∞ (\ displaystyle f (x) = O (g (x)) (\ text (as)) x \ to \ infty) </Dd> </Dl> <Dd> f (x) = O (g (x)) as x → ∞ (\ displaystyle f (x) = O (g (x)) (\ text (as)) x \ to \ infty) </Dd> <P> if and only if for all sufficiently large values of x, the absolute value of f (x) is at most a positive constant multiple of g (x). That is, f (x) = O (g (x)) if and only if there exists a positive real number M and a real number x such that </P> <Dl> <Dd> f (x) ≤ M g (x) for all x ≥ x 0 . (\ displaystyle f (x) \ leq \; Mg (x) (\ text (for all)) x \ geq x_ (0).) </Dd> </Dl>

Difference between big o notation and small o notation