The Degrees of Discontinuity of some Translators Between Representations of the Real Numbers
Representations like decimal representation are used for defining computability on the set of real numbers. Translatability between different representations has been studied in the past by several authors. Most of the not computably solvable translation problems are not even continuously solvable. In this paper the degrees of discontinutity of translations between a number of common representations are compared and characterized. Mainly three degrees are considered: the first one with translations between the standard representation and the weak cut representations, the second one contains among others the translations between m-adic und n-adic representations, and the third one contains translations concerning proper cut representations and the iterated fraction representation.
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