Contents Abstract 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; 01g alternatingly.
We speculate on the Gauian function [x] as an example of a non-continuous function which is nevertheless possessed of some properties of com-putability. 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… (More)
We will speculate on some aspects of computability of the system of Rademacher functions, a system of step functions on the compact interval [0; 1), jumping at nitely many binary rationals and assuming values f1; 01g. Knowledge in the notion of computability of a real number or a sequence of real numbers will be assumed. (A real number is computable if it… (More)
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.