class existence theorem (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun Phrase

Phonetic Transcription

/klæs ɪɡˈzɪstəns ˈθiːərəm/

Meaning and Usage

The term "class existence theorem" refers to a theorem in mathematical logic and category theory that asserts the existence of certain classes or structures under specific conditions or axioms. It's commonly used in advanced mathematics, particularly in discussions on set theory and type theory. The phrase is more likely found in written contexts, especially in academic papers and textbooks, given its technical nature.

Frequency of Use

“Class existence theorem” is not a commonly encountered phrase in day-to-day conversation. Its use is mainly restricted to mathematical, philosophical, or logical discussions, making it relatively infrequent outside of specialized academic literature.

Example Sentences

1. The mathematician proved the class existence theorem, which significantly advanced the field of category theory.

2. Математик доказал теорему существования классов, что значительно продвинуло область теории категорий.

3. Understanding the implications of the class existence theorem requires a solid background in set theory.

4. Понимание последствий теоремы существования классов требует прочной базы в теории множеств.

5. The lecture focused on applying the class existence theorem to various logical frameworks.

6. Лекция была сосредоточена на применении теоремы существования классов к различным логическим структурам.

Idiomatic Expressions

While “class existence theorem” does not have common idiomatic expressions associated with it, the terms "class" and "existence" might appear in various idiomatic contexts on their own. Here are a few idioms that could relate, albeit indirectly:

1. In a class of its own: The new software is in a class of its own when it comes to user-friendly design.

2. Новое программное обеспечение находится в своем классе, когда дело доходит до удобного дизайна.

3. Existential crisis: She felt she was going through an existential crisis after college, questioning her purpose in life.

4. Она чувствовала, что переживает экзистенциальный кризис после колледжа, задаваясь вопросом о своем предназначении в жизни.

5. Get a life: After endlessly playing video games, he was told to get a life and pursue more fulfilling interests.

6. После бесконечных часов игры в видеоигры ему сказали "займись жизнью" и займись более увлекательными интересами.

Etymology

The term "class" originates from the Latin word "classis," meaning a division or category. "Existence" comes from the Latin "existentia," meaning being or living. "Theorem" is derived from the Greek word "theorema," meaning a proposition that can be proven based on previously established statements.

Synonyms and Antonyms

Synonyms

• Existence theorem
• Existence proof

Antonyms

• Non-existence
• Absence theorem

This comprehensive overview provides detailed information about the term "class existence theorem," reflecting its significance in the mathematical discourse.