Informally, the term asymptotic means approaching a value or curve arbitrarily closely (i.e., as some sort of limit is taken). A line or curve that is asymptotic to given curve is called the asymptote of .
More formally, let be a continuous variable tending to some limit. Then a real function and positive function are said to be asymptotically equivalent, written , if
(1)

as the limit is taken.
Equivalently, consider the littleo asymptotic notation that is one of the Landau symbols. Then means that
(2)

as a limit is taken. The statement is then equivalent to
(3)

or
(4)

(Hardy and Wright 1979, pp. 78).
These definitions can also be applied to the discrete case of an integer variable that tends to infinity, a real function of , and a positive function of .