asymptotic value (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun

Phonetic Transcription

/æˌsɪmpˈtɒtɪk ˈvæljuː/

Meaning and Usage

"Asymptotic value" refers to a value that a function approaches as the input approaches a limit, often used in mathematical analysis, particularly in the context of calculus and graph theory. It indicates the behavior of a function as it reaches infinity or a critical point.

• Frequency of Use: The term is used mainly in advanced mathematical, statistical, or scientific contexts, making it more prevalent in written texts than in oral speech. Its usage is typically confined to academic and professional discussions.

Example Sentences

1. The asymptotic value of the function can be determined by analyzing its limit behavior.

2. Значение функции при асимптотическом приближении может быть определено путем анализа ее предельного поведения.

3. In the study of algorithms, understanding the asymptotic value helps predict performance as the input size grows.

4. В изучении алгоритмов понимание асимптотического значения помогает предсказать производительность с ростом размера входных данных.

5. The researchers concluded that the asymptotic value provides a more accurate representation in their models.

6. Исследователи пришли к выводу, что асимптотическое значение дает более точное представление в их моделях.

Idiomatic Expressions

The phrase "asymptotic value" is not commonly used in idiomatic expressions since it is a technical term primarily used in mathematical contexts. Therefore, examples of idiomatic expressions featuring this term are limited.

However, related mathematical terms might have idiomatic usage in specific contexts. Here are some broader mathematical idioms that include related concepts:

1. "Push the envelope" - Often used in mathematics and engineering to indicate pushing boundaries in research or computation.
2. Pushing the envelope in mathematics leads to new discoveries.

3. Прокладывание пути в математике ведет к новым открытиям.

4. "The limit does not exist" - A phrase that has gained cultural significance, usually in the context of discussions about boundaries or constraints.

5. In calculus, when faced with complex functions, you might say, "The limit does not exist!"

6. В математике, сталкиваясь со сложными функциями, вы можете сказать: "Предела не существует!"

7. "Finding common ground" - This expression can apply to finding a common value or solution in mathematical discussions.

8. When solving equations, we strive for finding common ground to simplify the problem.
9. При решении уравнений мы стремимся найти общую точку, чтобы упростить задачу.

Etymology

The term "asymptotic" originates from the Greek word "asumptotos", meaning "not falling together," referring to lines that approach each other but never touch. The word "value" derives from the Latin "valere," meaning "to be strong" or "to be worth." Together, "asymptotic value" represents values approached by functions under certain mathematical conditions.

Synonyms and Antonyms

• Synonyms: Limit value, approaching value, theoretical value.
• Antonyms: Divergent value, unbounded value (in contexts where a function does not converge).

This detailed breakdown of "asymptotic value" emphasizes its importance in mathematical discussions and illustrates how it is distinct from more common English expressions.