Definition for "Associative Law" in the Quantum Dictionary

- Natural & Formal Sciences -

Mathematics & Logic Dictionary

The law that the way operands are grouped in repeated application of a binary operator does not affect the result; formally, for operator ⊗ and operands A, B, C: (A ⊗ B) ⊗ C = A ⊗ (B ⊗ C) (example: (A ∧ B) ∧ C = A ∧ (B ∧ C)).

- Mathematics & Logic -

Pure Mathematics Dictionary

A binary operation * on a set satisfies the associative law if for all a,b,c one has (a*b)*c = a*(b*c); the placement of parentheses does not affect the result of successive applications of the operation.

- Pure Mathematics -

Algebra Dictionary

The algebraic property of a binary operation whereby the grouping (parenthesization) of operands does not change the result: for all a, b, c in the domain, (a·b)·c = a·(b·c).