But that is exactly the point. This problem deals with a formal definition.
Now I know that this is a personal peeve of mine.
I give Charles Pinter full credit for making me aware of this problem.
It is a notational problem.
Suppose that and what sense does it make to write
I agree with him, it makes no sense. But I disagree with his notation.
He uses for .
And if then is used for .
I suggested the more intuitive notations but never got any real takers.
I actually like that notation it makes more sense. I guess the real idea is that given a function you have automatically induced a natural function and then once you have that nasty notational buisness out of the way you can say and not have people wonder why a function which maps elements of a set is now mapping full subsets of that set.