I really overthought this. So that condition is really just the definition of a function H->H; H contains every element in the domain and range of k and there must be a k(y) in H for every element y in H. So that definition starting with the element e completely populates H as I mentioned...
Want to understand how set C contains ##N## x H. H is only defined to be a set with element e and as the domain/range of function k. Is this enough information to conclude that the second set in the cartesian product W is H and not a subset of H?
My thinking is to show that ##N## and H satisfy...