Commutativity is the ability to change the order of something without changing the end result.
A binary operation ∗ on a set S is commutative if:
- $ \forall x,y \in S: x * y = y * x \, $
A binary function f:A×A → B is commutative if:
- $ \forall x,y \in A: f (x, y) = f(y, x) \, $