A Logical Calculus To Intuitively And Logically Denote Number Systems
General Mathematics
2021-02-05 v9
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.
Cite
@article{arxiv.0805.3266,
title = {A Logical Calculus To Intuitively And Logically Denote Number Systems},
author = {Pith Xie},
journal= {arXiv preprint arXiv:0805.3266},
year = {2021}
}
Comments
29 pages; to appear, Progress in Applied Mathematics. Vol 1, No 2 (2011), 43-70