anticommutative

Meanings

• adjective

  In mathematics, a binary operation is said to be anticommutative if x * y does not equal y * x for at least one pair of operands x and y.

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Variants

List of all variants of anticommutative that leads to same result
anticompetitive

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Etymology

origin and the way in which meanings have changed throughout history.

The term 'anticommutative' comes from the Latin words 'antikommutare', which means 'to exchange reciprocally' or 'to commute in the opposite direction'. In mathematics, the term is used to describe a binary operation that does not follow the commutative property.

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Trivia

Any details, considerations, events or pieces of information regarding the word

1. Did you know that multiplication of matrices is an example of an anticommutative binary operation?

2. The term 'anticommutative' is often used in the context of group theory and algebra.

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Related Concepts

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1. Commutative property: In mathematics, the commutative property is a property of some binary operations where the order of the operands does not matter. For example, in addition, the commutative property states that a + b = b + a for all real numbers a and b. In contrast, anticommutative binary operations do not follow this property.

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How to Memorize "anticommutative"

1. visualize
   

   - To visualize an anticommutative binary operation, imagine swapping the operands in the equation and observing a difference in the result.

2. associate
   

   - To memorize the meaning of 'anticommutative', associate it with the idea of a binary operation that does not follow the commutative property.

3. mnemonics
   

   - A possible mnemonic for 'anticommutative' is 'Anti' for 'Anticommutative' and 'commutative' for 'Commutes'. Remember that 'Anti-commutes' not 'commutes'.

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