 TOPICS # Asymptotic

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 little-o 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. 7-8).

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 .

Asymptosy, Asymptote, Asymptotic Curve, Asymptotic Direction, Asymptotic Notation, Asymptotic Series, Big-O Notation, Landau Symbols, Limit, Little-O Notation, Order of Magnitude

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## References

Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 7-8, 1979.

Asymptotic

## Cite this as:

Weisstein, Eric W. "Asymptotic." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Asymptotic.html