Let 
be an integer variable which tends to infinity and let 
be a continuous variable tending to some limit. Also, let
or 
be a positive function and 
or 
any function. Then Hardy and Wright (1979) define
1. 
to mean that 
for some constant 
and all values of 
and 
,
2. 
to mean that 
,
3. 
to mean that 
,
4. 
to mean the same as 
,
5. 
to mean 
,
and
6. 
to mean 
for some positive constants 
and 
.
implies and is stronger than 
.
The term Landau symbols is sometimes used to refer the big-O notation 
and little-O notation 
. In general, 
and 
are read as "is of order 
."
If 
,
then 
and 
are said to be of the same order of magnitude
(Hardy and Wright 1979, p. 7).
If 
,
or equivalently 
or 
,
then 
and 
are said to be asymptotically equivalent (Hardy and Wright 1979, p. 8).
