Non-negative Rational Semantic Numeration Systems
Alexander Chunikhin
TL;DR
This paper introduces positive rational Semantic Numeration Systems, analyzing their properties as dynamical systems and proposing initial ideas for partial integer systems.
Contribution
It presents a new class of Semantic Numeration Systems based on positive rational numbers and explores their properties and potential for partial integer systems.
Findings
Properties of positive rational Semantic Numeration Systems as dynamical systems are formulated.
Differences in carry and remainders are defined for cardinal semantic operators.
Analytical and numerical examples illustrate the systems' behavior.
Abstract
A new class of Semantic Numeration Systems, namely, positive rational Semantic Numeration Systems is introduced. For cardinal semantic operators, differences in the formation of carry (common carry) and remainders are defined. The properties of positive rational Semantic Numeration Systems as dynamical systems are formulated and illustrated through analytical and numerical examples. A first attempt at defining partial integer Semantic Numeration Systems is proposed.
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