Uniqueness summary and idea

[jaydfox]

Same effect, however, so there's no practical difference, simply different implementation methods. For the converging series, to get some level of precision, you need to compute the first m terms of the series, where m dependings on the precision desired and the input x. For the non-converging series, to get some level of precision, you need to compute the first k terms within some radius, then use j integer iterations using i_j terms to get back to the desired input. In either case, a given level of precision at a given input requires a determinable number of calculations, and exact precision in either case requires an infinite number of calculations (unless the power series is finite).