Commutative Operations

Why

We introduce language for the case in which an operation does not depend on the order in which it operates.

An operation commutes if the result of two elements is the same regardless of their order.

Let $A$ be a non-empty set and let $+: A \times A \to A$ be an operation. If $+$ commutes, then

\[ a + b = b + a \]

for all $a, b \in A$.