Commutativity (idea)

A property that some binary operations possess. The operation @ is commutative if for all a,b, the following holds:

a@b = b@a

Examples:

• addition, XOR
• multiplication
• max (including logical OR)
• min (including logical AND)
• Define a#b to be the number of appearances of 42 among a,b. It is easy to verify # is commutative. But it lacks associativity, which shows (along with, say, matrix multiplication) that there is no connection between the two concepts.

Non examples:

• subtraction
• division
• matrix multiplication
• exponentiation