On-line digit set conversion in real base

On-line digit set conversion in real base

Let be a real number > 1. The digit set conversion between real numbers represented in xed base is shown to be computable by an on-line algorithm, and thus is a continuous function. When is a Pisot number the digit set conversion is computable by an on-line nite automaton.

On-Line Addition in Real Base

Let be a real number > 1. Addition and multiplication by a xed positive integer of real numbers represented in base are shown to be computable by an on-line algorithm, and thus are continuous functions. When is a Pisot number, these functions are computable by an on-line nite automaton.

On-Line Multiplication in Real and Complex Base

Multiplication of two numbers represented in base is shown to be computable by an on-line algorithm when is a negative integer, a positive non-integer real number, or a complex number of the form ipr, where r is a positive integer.

Set Theory, Forcing and Real Line

We give a very brief survey on ZFC theory (Zermelo-Fraenkel Set Theory) and we present an intuitive introduction to the method of forcing and some applications to the real line. Our exposition will be very informal, without any claim of completeness and rigour. The idea is just to give a very intuitive idea of what Set Theory and forcing-method are, and why they are interesting and useful from ...

Digit On-line Large Radix CORDIC Rotator