Given a set A you can define an operation on it. Let ◌ denote an arbitrary operation.
◌ assigns a two elements A,B one element A◌B and A◌B belongs to A
For ◌ to be an operation on A some criteria has to be met:
-a◌b has to be define for all pairings of elements in A.
-a◌b is uniquely defined (one to one)
-closure under ◌ in other words, if a and b are in A then a◌b must also be in A
