I think however what you probably are looking at is a convergent sequence of functions. Even this is not that simple. A convergent sequence of functions can be pointwise Divergent functions are basically two functions whose difference of values for large values of their domain will grow larger.
Summary points on divergent and convergent thinking. Both divergent and convergent thinking are essential in problem solving. Divergent thinking leaves room for ambiguity while convergent thinking strongly focuses on the exact answer. As compared to convergent thinkers, divergent thinkers tend to have better moods.