nonassociative

Thân thiện

The equation uses a nonassociative operation.

Definition

1. 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) - 1 is not equal to 5 - (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

Học thuật

Adjective

1. not associative