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Definitions from the Web

Asymptotically

Definition

Asymptotically refers to a mathematical concept that describes the behavior of a function or a sequence as it approaches a certain limiting value or infinity. Asymptotic behavior implies that the function or sequence gradually approaches the limiting value without ever reaching it.

Senses

• Adverb: Referring to the asymptotic behavior of a function or sequence.

Usage

Asymptotically can be applied in various contexts:

Mathematics

In mathematics, when studying functions or sequences, one might observe how they behave asymptotically.

For example:

1. The function f(x) = 1/x has an asymptotic behavior of approaching zero as x tends to infinity.
2. The sequence {2^n} grows asymptotically as n increases.

Computer Science

In computer science, algorithms often have an asymptotic analysis to determine their time complexity:

For example:

• An algorithm with a time complexity of O(n^2) is asymptotically less efficient than an algorithm with a time complexity of O(n log n) as the input size increases.

Physics

In physics, asymptotically can describe the behavior of physical quantities:

For example:

• The distance between two masses decreases asymptotically as they approach each other due to gravitational attraction.

Related Products

If you are interested in learning more about asymptotic analysis in computer science:

• Asymptotic Analysis in Computer Science