A Logical Calculus To Intuitively And Logically Denote Number Systems

Details A Logical Calculus To Intuitively And Logically Denote Number Systems A Logical Calculus To Intuitively And Logically Denote Number Systems

2008-05-21

arxiv.org/abs/0805.3266v18

Mathematics

General Mathematics

29 pages; to appear, Progress in Applied Mathematics. Vol 1, No 2 (2011), 43-70

Scientific paper

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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