The average $a \ast b = \frac{a + b}{2}$ of two real numbers
Terms
| Term | This example | Why |
|---|---|---|
| commutative | ✓ | The average of two numbers is commutative, because $\frac{a + b}{2} = \frac{b + a}{2}$. |
| associative | ✗ | The average of two numbers is not associative, because $(0 \ast 0) \ast 4 = 0 \ast 4 = 2$, but $0 \ast (0 \ast 4) = 0 \ast 2 = 1$. |
Distinctions using this example
- Associative vs. commutative: The average of two numbers shows that a commutative operation need not be associative.