Real numbers, continued fractions and complexity classes
Some representations of real numbers (including Cauchy sequences of rationals, Dedekind cuts and variants, and continued fractions) are studied from both the viewpoint of recursive functionals and of complexity theory. Complexity arguments are used also to make explicit the impossibility of obtaining some functions as recursive functionals. It is also shown that representations of real numbers that are equivalent from the viewpoint of recursive functionals are clearly different from the viewpoint of complexity. Continued fractions are studied in a more detailed way. The authors claim that Cauchy sequences of rationals are ``the unique representation of real numbers suitable for the ordinary calculus''.
scientific article; zbMATH DE number 4177051