Other approaches

are briefly discussed in Chapter 7 below. They consist of the use of more sophisticated notations for real numbers, such as Cauchy sequences of dyadic rationals with fixed rate of convergence, continued fractions, and infinite compositions of Möbius transformations. From the point of view of efficiency, some approaches are better than others for some problems, and worse than others for other problems. However, much of the theory of exact real number computation is independent of the particular notation systems under consideration.