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) \,

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