Definition:Associative

Definition
Let $\circ$ be a binary operation.

Then $\circ$ is defined as being associative on $S$ iff:


 * $\forall x, y, z \in S: \left({x \circ y}\right) \circ z = x \circ \left({y \circ z}\right)$

Also see

 * Associativity on Four Elements
 * General Associativity Theorem

Historical Note
The term associative was coined by William Hamilton in about 1844 while thinking about octonions, which aren't.