Abstract Math. More Practice with Associativity. 

We look at some unusual binary operations and think about whether or not they are associative. The first example is EQUALS on the integers: EQUALS(x,y) = 1, if x = y, and 0 if x is not equal to y. This turns out to be associative, but the proof is difficult. Similarly, the finite binary opbinary operations we defined on finite sets earlier need to be investigated.