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 
.
