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

Part of Speech

Noun

Phonetic Transcription

/ˌæsɪmˈtoʊtɪk pɔɪnt/

Meaning and Usage

The term "asymptotic point" refers to a position or value towards which a function approaches as the input or variable approaches a certain limit, often at infinity. This is a term commonly used in mathematics, particularly in calculus and analysis, to describe the behavior of functions.

In more general terms, it conveys the idea of a limit that is never actually reached but can be approached indefinitely. The phrase is mostly used in written contexts, especially in mathematical discussions, literature, or scientific papers. It is encountered relatively frequently in academic settings.

Example Sentences

1. The function exhibits asymptotic points as it approaches infinity, indicating its limiting behavior.

2. Функция демонстрирует асимптотические точки по мере приближения к бесконечности, указывая на ее предельное поведение.

3. Understanding asymptotic points is crucial for predicting the long-term behavior of algorithms.

4. Понимание асимптотических точек имеет решающее значение для прогнозирования долгосрочного поведения алгоритмов.

5. In statistics, we often look at the asymptotic point to assess the efficiency of estimators.

6. В статистике мы часто рассматриваем асимптотическую точку для оценки эффективности оценивателей.

Idiomatic Expressions

The term "asymptotic point" does not feature prominently in common idiomatic expressions in English. However, the concept of asymptotic behavior is often discussed in contexts that relate to limits and endpoints.

Example Idiomatic Sentences

1. As he approached the asymptotic point of exhaustion, he pushed through to finish the marathon.

2. Подходя к асимптотической точке истощения, он продолжал двигаться, чтобы закончить марафон.

3. The project reached an asymptotic point of improvement, and further efforts yielded diminishing returns.

4. Проект достиг асимптотической точки улучшений, и дальнейшие усилия приносили все меньше результатов.

5. In our discussion about climate change, we reached an asymptotic point where solutions became less effective.

6. В нашем обсуждении изменения климата мы достигли асимптотической точки, где решения стали менее эффективными.

Etymology

The word "asymptotic" derives from the Greek word "asumptotos," which means "not falling together." The root "symptote" refers to a line that a curve approaches as it heads towards infinity, highlighting the concept of limit in mathematical analysis.

Synonyms and Antonyms

Synonyms

• Limiting point
• Limit point
• Converging point

Antonyms

• Divergent point
• Unbounded point
• Extending point

This comprehensive information provides various perspectives on the term "asymptotic point," ensuring a thorough understanding of its usage and significance in different contexts.