Big-O notation, written 
and pronounced "big-O of 
," uses 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 a specified 
or to 
or 
, if 
and 
are positive functions,
and if 
and 
are arbitrary functions, then it is said that 
provided that 
for some positive constant 
, for all sufficiently large 
, or for all 
in a punctured neighborhood
of 
in the finite case, or sufficiently large in the indicated direction in the infinite
case.
For eventually nonnegative real-valued functions 
and positive functions 
, big-O notation and big-omega
notation satisfy
 |
Additionally, big-O notation is related to little-O notation in that 
is stronger than and implies 
.
