Navigating Number Systems for Computational Precision: An Analytical Exploration

Abstract

The main objective of this article is to study all numbers that have occurred so far in the theoretical discussions were real (or complex) numbers in the strict mathematical sense. That is, they were to be conceived as infinite decimal fractions, or as Dedekind cuts. For the purposes of computation such numbers have to be approximated by real numbers of a rather special type, such as terminating decimal fractions, or other rational numbers. The present article is devoted to a study of the number systems that can be used for the purpose of computation.