Big-O Notation

The symbol , pronounced "big-O of ," is one of the Landau symbols and is used to symbolically express the asymptotic behavior of a given function.

In particular, if  is an integer variable which tends to infinity and  is a continuous variable tending to some limit, if  and  are positive functions, and if  and  are arbitrary functions, then it is said that provided that  for some constant  and all values  and .

Note that Big-O notation is the inverse of Big-Omega notation, i.e., that

Additionally, Big-O notation is related to Little-O notation in that  is stronger than and implies .