Physicists and engineers use the phrase "order of magnitude" to refer to the smallest power of ten needed to represent a quantity. Two quantities 
and 
which are within about a factor of 10 of each other are then
said to be "of the same order of magnitude," written 
.
Hardy and Wright (1979, p. 7) say a real function 
and positive function 
with continuous variable 
that tends to some limit are of the same order of magnitude,
written using asymptotic notation as 
, if 
for positive constants 
and 
independent of 
. This term is also used for 
an integer variable that tends to infinity, a real function
,
and a positive function 
.
