asymptotic Definition
relating to or approaching a value or curve arbitrarily closely, but never meeting it.
Using asymptotic: Examples
Take a moment to familiarize yourself with how "asymptotic" can be used in various situations through the following examples!
Example
The two lines are asymptotic and will never intersect.
Example
As x approaches infinity, the function becomes asymptotic to the y-axis.
Example
The growth rate of the population is asymptotic to the carrying capacity of the environment.
asymptotic Synonyms and Antonyms
Synonyms for asymptotic
Phrases with asymptotic
a property of some theories in physics, where the force between particles decreases as they move closer together
Example
Asymptotic freedom is a key feature of quantum chromodynamics.
a way of describing the limiting behavior of a function, often used in computer science to analyze algorithms
Example
Big O notation is a common form of asymptotic notation.
a mathematical series that represents a function as an infinite sum of terms, often used in calculus and analysis
Example
The Taylor series is an example of an asymptotic series.
Origins of asymptotic
from Greek 'asumptotos', meaning 'not falling together'
Summary: asymptotic in Brief
'Asymptotic' [ˌeɪsɪmˈtɒtɪk] describes a relationship between values or curves that approach each other arbitrarily closely, but never meet. It is often used in mathematics and physics to describe the behavior of functions or particles. Phrases like 'asymptotic notation' and 'asymptotic series' refer to specific mathematical concepts that use this idea. 'Asymptotic freedom' is a property of some theories in physics where the force between particles decreases as they move closer together.
