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arXiv · 0805.3266

A Logical Calculus To Intuitively And Logically Denote Number Systems

Pith Xie
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Abstract

Simple continued fractions, base-b expansions, Dedekind cuts and Cauchy sequences are common notations for number systems. In this note, first, it is proven that both simple continued fractions and base-b expansions fail to denote real numbers and thus lack logic; second, it is shown that Dedekind cuts and Cauchy sequences fail to join in algebraical operations and thus lack intuition; third, we construct a logical calculus and deduce numbers to intuitively and logically denote number systems.

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Pith Xie. 2008-05-21. A Logical Calculus To Intuitively And Logically Denote Number Systems. https://arxiv.org/abs/0805.3266

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