little-O

The symbol o(x), pronounced "little-O of x, " is one of the Landau symbols and is used to symbolically express the asymptotic behavior of a given function. In particular, if n is an integer variable which tends to infinity and x is a continuous variable tending to some limit, if ϕ(n) and ϕ(x) are positive functions, and if f(n) and f(x) are arbitrary functions, then it is said that f element o(ϕ) provided that f/ϕ->0. Thus, ϕ(n) or ϕ(x) grows much faster than f(n) or f(x). Note that little-O notation is the inverse of little-omega notation, i.e., that f(n) element o(ϕ(n)) ⟺ ϕ(n) element ω(f(n)).

asymptotic | asymptotic notation | big-omega notation | big-O notation | big-theta notation | Landau symbols | little-omega notation