completely reducible set (english) - meaning, definition, translation, pronunciation

Part of Speech

• Noun Phrase

Phonetic Transcription

• /kəmˈpliːtli rɪˈdjuːsibəl sɛt/

Meaning and Usage

A completely reducible set refers to a set of mathematical objects (often within the realms of algebra or group theory) that can be entirely decomposed into simpler components. In this context, "completely reducible" indicates that every element of the set can be expressed in terms of more fundamental elements or sub-structures.

This term is mainly used in written and academic contexts, particularly in mathematical literature. Its frequency of use is confined to specialized fields, with less prevalence in everyday language or oral discourse.

Example Sentences

1. The mathematician proved that the given algebraic structure is a completely reducible set.

2. Математик доказал, что данная алгебраическая структура является полностью редуцируемым множеством.

3. In group theory, a completely reducible set can simplify the analysis of symmetries in geometric objects.

4. В теории групп полностью редуцируемое множество может упростить анализ симметрий в геометрических объектах.

5. The properties of the completely reducible set help in understanding the underlying structure of the mathematical model.

6. Свойства полностью редуцируемого множества помогают понять основную структуру математической модели.

Idiomatic Expressions

While "completely reducible set" itself does not appear frequently in idiomatic expressions, the concept of "reducibility" can be related to several phrases in mathematics and philosophy that signify simplification or fundamental elements.

Example Idiomatic Expressions

1. "Reducible to fundamentals" - This suggests stripping away complexities to focus on basic principles.
2. It's essential to reduce the problem to fundamentals to find an effective solution.

3. Необходимо свести проблему к основным принципам, чтобы найти эффективное решение.

4. "Reduce to the essence" - To condense a situation or argument to its most important aspects.

5. When discussing the project, we need to reduce it to the essence of what we aim to achieve.

6. При обсуждении проекта нам необходимо свести его к сути того, чего мы хотим достичь.

7. "To break it down" - To simplify or analyze something by dividing it into smaller parts.

8. Let’s break it down into manageable tasks to understand it better.
9. Давайте разобьем это на управляемые задачи, чтобы лучше понять.

Etymology

The term "completely reducible set" derives from mathematical terminology. "Completely" comes from the Latin completus, meaning "filled up" or "finished," while "reducible" originates from the Latin reducere, which means "to bring back, restore," indicating its ability to be simplified. "Set" comes from the Middle English setten, meaning "to place."

Synonyms and Antonyms

• Synonyms: fully decomposable set, entirely reducible group
• Antonyms: irreducible set, indivisible group

In mathematical discourse, understanding the nuances between these terms can be critical, especially when dealing with complex structures.