Commutative: meaning, definitions and examples
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commutative
[ kəˈmjuːtətɪv ]
mathematics property
In mathematics, a binary operation is said to be commutative if changing the order of the operands does not change the result. This property is most commonly associated with addition and multiplication in arithmetic. For example, in the case of addition, 3 + 4 is the same as 4 + 3. The concept of commutativity can also be applied in other areas such as algebra and set theory. Understanding commutative properties is crucial in simplifying expressions and solving equations.
Synonyms
Examples of usage
- 3 + 5 = 5 + 3
- Multiplication is commutative: 6 * 2 = 2 * 6
- In set theory, the union of sets is commutative.
Translations
Translations of the word "commutative" in other languages:
🇵🇹 comutativa
🇮🇳 संक्रमणीय
🇩🇪 kommutativ
🇮🇩 komutatif
🇺🇦 комутативний
🇵🇱 komutacyjny
🇯🇵 可換の
🇫🇷 commutatif
🇪🇸 conmutativo
🇹🇷 komütatif
🇰🇷 가환의
🇸🇦 تبادلي
🇨🇿 komutativní
🇸🇰 komutatívny
🇨🇳 交换的
🇸🇮 komutativni
🇮🇸 samhverf
🇰🇿 айырбастау
🇬🇪 კომუტატიური
🇦🇿 komutativ
🇲🇽 conmutativo
Etymology
The term 'commutative' originates from the Latin word 'commutare', which means 'to interchange' or 'to exchange'. The roots of 'commutare' are 'com-' (together) and 'mutare' (to change). The use of the term in a mathematical context began to gain prominence in the 19th century when mathematicians started to formalize the properties of operations. Initially associated with arithmetic, the notion of commutativity expanded to various branches of mathematics, including algebra and abstract algebra. The importance of this property lies in its ability to simplify calculations and proofs, making it a fundamental concept in mathematical theory.