Rational and algebraic Q_2-representation of real numbers

Author:

Mykola~Pratsovytyi,~Oleg~Makarchuk,~Sofia~Skrypnyk

2010 Mathematics Subject Classification:

11H71.

Keywords:

classic binary expansion, Q_2-representation of numbers, rational Q_2-representation, two-symbol representation.

Abstract:

We consider rational and algebraic Q_2-representations of the fractional part of a real number generalizing the classic binary representation. We specify probabilistic problems leading to this concept, prove sufficient condition of rationality of a number and reject a hypothesis that a criterion of rationality for rational Q_2-representation of a number is completely analogous to the known criterion of rationality for binary representation. We construct a rational number having a non-periodic Q_2-representation.

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Vol. 10 (18), 2015