Asymptotically is a term that is often used in mathematics and science. It refers to a situation where two values or functions approach each other but never quite meet. This term is commonly used in calculus, where it is used to describe the behavior of functions as they approach a limit. In this article, we will explore the definition and meaning of asymptotically, as well as its origins, associations, synonyms, and antonyms.
Definitions
Asymptotically is an adverb that describes a situation where two values or functions approach each other but never quite meet. It is used to describe the behavior of a function as it approaches a limit. In mathematics, the term is used to describe the behavior of a function as the input variable approaches infinity or some other limit.
Origin
The term asymptotically comes from the Greek word “asymptotos,” which means “not falling together.” The word was first used in mathematics in the 17th century by the French mathematician Pierre de Fermat.
Meaning in different dictionaries
The meaning of asymptotically is consistent across different dictionaries. It is defined as “approaching a value or curve without ever meeting it.” Some dictionaries also include a mathematical definition, describing it as the behavior of a function as the input variable approaches infinity or some other limit.
Associations
Asymptotically is commonly associated with calculus and other branches of mathematics. It is also used in science, particularly in physics and engineering, to describe the behavior of systems as they approach a limit.
Synonyms
Synonyms of asymptotically include “approaching,” “nearing,” “converging,” and “tending toward.”
Antonyms
Antonyms of asymptotically include “diverging,” “deviating,” and “moving away from.”
The same root words
There are no other words with the same root as asymptotically.
Example Sentences
- The function approaches zero asymptotically as x approaches infinity.
- The two curves approach each other asymptotically but never quite meet.
- The system will converge asymptotically to its steady-state solution.