(definition)
Definition: A function where f(A, f(B, C)) = f(f(A, B), C).
See also commutative.
Note:
Multiplication is associative, e.g., 2 × (3 × 4) = (2 × 3) × 4, and commutative, e.g., 2 × 3 = 3 × 2. Subtraction is neither associative, e.g., 2 - (3 - 4) ≠ (2 - 3) - 4, nor commutative, e.g., 2 - 3 ≠ 3 - 2. Because of rounding floating point addition on a computer is not associative, e.g., (1000000 + .00001) + .00001 ≠ 1000000 + (.00001 + .00001) (actual values depend on the details of the computer addition), but is commutative, e.g., 1000000 + .00001 = .00001 + 1000000.
Cartesian product is associative, e.g., {1, 2} × ({a, b} × {X, Y}) = ({1, 2} × {a, b}) × {X, Y}, but is not commutative, e.g., {1, 2} × {a, b} ≠ {a, b} × {1, 2}.
Author: PEB
If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.
Entry modified Fri Dec 17 12:02:15 2004.
HTML page formatted Wed Oct 26 09:47:12 2005.
Cite this as:
Paul E. Black, "associative", from
Dictionary of Algorithms and Data
Structures, Paul E. Black, ed.,
NIST.
http://www.nist.gov/dads/HTML/associative.html
