nonassociative
Definition
- Adjective:
- Not associative: Describes an operation or algebraic structure where the associative property does not hold. This means that the way elements are grouped in an operation affects the result.
Usage
- The term "nonassociative" is primarily used in formal contexts, especially in mathematics, logic, and computer science, to describe operations or systems where the grouping of operands changes the outcome.
- It is the direct negation of "associative." An operation is associative if for all . An operation is nonassociative if this equality is not guaranteed.
Examples
- Adjective:
- Subtraction is a nonassociative operation because
(5 - 3) - 1is not equal to5 - (3 - 1). - The cross product in vector algebra is another example of a nonassociative operation.
- Researchers are studying nonassociative algebras, which have applications in theoretical physics.
Advanced Usage
- Nonassociative Algebra: A branch of algebra dealing with algebraic structures where multiplication is not required to be associative. Examples include Lie algebras, Jordan algebras, and octonions.
- Nonassociative Learning: In psychology and neuroscience, this refers to a simple form of learning (like habituation or sensitization) that does not involve forming associations between multiple stimuli or events.
Variants and Related Words
- Nonassociativity (noun): The property or condition of being nonassociative.
- The nonassociativity of subtraction complicates the order of calculations.
- Associative (adjective): The opposite property, where grouping does not affect the result.
Synonyms
- Not associative (formal definition)
- Grouping-sensitive (descriptive, less common)
Antonyms
- Associative
Adjective
-
not associative
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