An internal operation ❄︎ on a set is commutative if, for all elements a and b of E, we have : a ❄︎ b = b ❄︎ a.
Example
The addition and multiplication of real numbers are commutative operations.
- 7 + 9 = 9 + 7
- 7 × 9 = 9 × 7
The subtraction of real numbers is not a commutative operation.
- 8 – 5 ≠ 5 – 8, since : 3 ≠ –3