Noun
/kənˈtɪn.ju.ə.ti ˈθiː.ə.rəm/
The "continuity theorem" is a term from mathematics, particularly in the field of real analysis and topology. It refers to the concept that under certain conditions, functions that are continuous behave in predictable ways. The most common use of the continuity theorem is in the context of proving properties about functions and their limits. It implies that a function that is continuous on a closed interval will achieve all values between its maximum and minimum.
This term is relatively technical and is primarily used in written academic and scientific contexts, rather than in casual oral speech.
Translation: Теорема непрерывности важна для понимания поведения функций в математическом анализе.
In my lecture, I explained the continuity theorem and its implications for integrals.
Translation: На моей лекции я объяснил теорему непрерывности и ее последствия для интегралов.
The continuity theorem underpins many fundamental theorems in mathematical analysis.
While "continuity theorem" is a specialized term, it is not typically used in idiomatic expressions. However, the concept of continuity can lead to discussions involving "staying the course" or "maintaining continuity." Below are a few sentences that incorporate the concept of continuity in a broader sense.
Translation: Нам нужно поддерживать непрерывность в нашем рабочем процессе, чтобы избежать каких-либо перебоев в проекте.
The company's strategy focuses on the continuity of leadership to ensure stability.
Translation: Стратегия компании сосредоточена на непрерывности руководства для обеспечения стабильности.
To achieve success, it is crucial to have continuity in both effort and vision.
The term "continuity" comes from the Latin word "continuus," meaning "uninterrupted." The word "theorem" derives from the Greek "theorema," which means "a proposition" or "something to be looked at." Together, they reflect the mathematical idea of an uninterrupted property in functions.
The "continuity theorem" itself is a specific mathematical term and is not commonly associated with direct synonyms or antonyms in everyday language but can be considered in the context of related mathematical concepts.