[Copypaste] various representations

Large O notation:

f (x) = O (g (x)) indicates that f (x) is the upper bound of G (x). The upper bound is not a definite answer. For example, the upper bound of n^2 can be n^3.

Actually O (g (x)) should be a collection of functions, so it should be written as f (x) ∈o (g (x)).

Small O notation:

f (x) = O (g (x)) indicates that f (x) is approaching g (x). For example F (x) =x^2+1, g (x) =x^2.

Ω notation:

F (x) =ω (g (x)) indicates that f (x) is the lower bound of g (x). For example, N (g (x)) is a lower bound of n^2 (f (x)).

Θ notation:

F (x) =θ (g (x)) indicates that g (X) is f (x) indeed bounded. That is, it satisfies both f (x) = O (g (x)) and F (x) =ω (g (x)).

symbols	definition
	Asymptotic upper Limit
	asymptotically Negligible ( ）
	The asymptotic lower bound (when and only if ）
	Asymptotically dominant (when and only if ）
	Asymptotically tight bound (when and only if And ）

Original: http://www.cnblogs.com/lzsz1212/p/3955218.html

http://www.aichengxu.com/view/2422583

[Copypaste] various representations