Irreducible: meaning, definitions and examples
🔍
irreducible
[ɪrɪˈdjuːsəbl ]
Definition
mathematics, general
The term 'irreducible' refers to something that cannot be reduced or simplified further. In mathematics, it often describes polynomial expressions that cannot be factored over a given set of numbers. For example, an irreducible fraction is one where the numerator and denominator have no common factors other than one. The concept can also apply to other fields, such as physics and chemistry, indicating elements or compounds that cannot be broken down into simpler substances. Its usage often implies a certain level of complexity that cannot be diminished.
Synonyms
indivisible, unbreakable, unsimplifiable.
Examples of usage
- An irreducible polynomial cannot be factored.
- The fraction 5/9 is irreducible.
- Some irreducible elements cannot be simplified further.
- We studied irreducible representations in group theory.
Interesting Facts
Mathematics
- In math, irreducible often refers to fractions or polynomials that cannot be simplified further.
- A prime number is considered irreducible because it cannot be divided by any other number except itself and one.
Science
- In physics, certain materials have irreducible properties that cannot be altered without changing their basic nature.
- The concept of irreducibility appears in quantum mechanics, where some particles cannot be split into simpler components.
Philosophy
- The idea of irreducibility can be seen in theories of consciousness, suggesting that human experience cannot be fully explained by physical processes alone.
- Philosophers discuss irreducibility in the context of moral truths that cannot be reduced to social or biological bases.
Literature
- In literature, some themes and narratives can be seen as irreducible in their complexity, capturing the depth of human experience.
- Irreducible characters are those who cannot be easily defined or categorized, often representing multifaceted aspects of life.
Pop Culture
- In popular video games, certain items or characters may be labeled as irreducible, indicating they can't be broken down or downgraded.
- Movies often include irreducible plot twists that change the story in ways that can't be simplified to 'what came before.'
Translations
Translations of the word "irreducible" in other languages:
🇵🇹 irredutível
🇮🇳 अपरिवर्तनीय
🇩🇪 irreduzibel
🇮🇩 tak tereduksi
🇺🇦 ірредуцований
🇵🇱 irredukcjonowalny
🇯🇵 還元不可能な
🇫🇷 irréductible
🇪🇸 irreducible
🇹🇷 indirgenemez
🇰🇷 불가역적인
🇸🇦 غير قابل للاختزال
🇨🇿 nepodmíněný
🇸🇰 neodvodený
🇨🇳 不可约的
🇸🇮 neizvedljiv
🇮🇸 óbreytanlegur
🇰🇿 азайтылмайтын
🇬🇪 არამწვდილი
🇦🇿 azaldılmağı mümkün olmayan
🇲🇽 irreducible