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- Mariko Yasugi, Masako Washihara
- Words, Languages & Combinatorics
- 2000

We will speculate on some computational properties of the system of Rademacher functions f n g. The n-th Rademacher function n is a step function on the interval [0; 1), jumping at nitely many dyadic rationals of size 1 2 n and assuming values f1; 1g alternatingly.

The major objective of this article is a refinement of treatments of the mutual relationship between two notions of “sequential computability” of a function which is possibly Euclidean-discontinuous, one using limiting recursion and one using effective uniformity. We also speculate on these methods from a mathematician’s viewpoint.

We speculate on the Gau ian function [x] as an example of a noncontinuous function which is nevertheless possessed of some properties of computability. An algorithm how to compute [x] for a single computable real number is rst described, followed by a remark that [x] does not necessarily preserve sequential computability. Second, [x] is studied in the light… (More)

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