A In previous sections it was pointed out that not always can the product of any two functions be made. The first function may carry elements where the second function cannot pick them up (range of the first function is not contained in the domain of the second function) to carry them to some third set. This lack of conformability never happens if only one set is involved, because the ranges are contained the domains which are the entire set.
[4.1a]
A transformation on a set is a function that carries elements of that set back onto elements in that same set.
[4.1b]
A transformation is a function whose range is contained in its domain.