ASSOCIATIVITY

Definition: An operation *, on a set G is associative if .

EXAMPLES

Addition and multiplication of numbers, i.e. elements of N, Z, Q, R or C, can be assumed to be associative.

Addition and multiplication of matrices can be assumed to be associative.

Composition of functions is also assumed to be associative.

COUNTEREXAMPLES

Subtraction is not associative.

Division is not associative.