Irreducible: meaning, definitions and examples
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irreducible
[ ɪrɪˈdjuːsəbl ]
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.
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
Etymology
The word 'irreducible' is derived from the prefix 'ir-', meaning 'not', and 'reducible', which comes from the Latin 'reducere', meaning 'to bring back'. The use of 'irreducible' in the mathematical context can be traced back to the 19th century when mathematicians began formalizing the properties of polynomials and other mathematical entities. Its applications extended beyond mathematics into physics and chemistry as the understanding of complex systems grew. This term emphasizes the concept that certain structures or equations maintain their form and cannot be simplified, showcasing the richness of mathematical theory and its implications in various scientific disciplines.