A Logical Calculus to Intuitively and Logically Denote Number Systems

Pith Xie

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. KeyWords: Number system; Logical calculus; Series

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DOI: http://dx.doi.org/10.3968%2Fj.pam.1925252820120102.004

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