An internal operation ❄︎ on a set

*E*is associative if, for all elements*a*,*b*and*c*in*E*, we have : (*a*❄︎*b*) ❄︎*c*=*a*❄︎ (*b*❄︎*c*).### Examples

The addition and multiplication of real numbers are associative operations.

- (12 + 14) + 16 = 12 + (14 + 16)
- (6 × 5) × 3 = 6 × (5 × 3)
- (
*x*+*y*) +*z*=*x*+ (*y*+*z*) - (
*x*×*y*) ×*z*=*x*× (*y*×*z*)

The subtraction of real numbers is not an associative property.

- (15 – 10) – 3 ≠ 15 – (10 – 3), since : 2 ≠ 8