Rethinking real numbers as infinite decimals
Logic
2021-08-05 v1 History and Overview
Abstract
We give a~detailed construction of the complete ordered field of real numbers by means of infinite decimal expansions. We prove that in the canonical encoding of decimals neither addition nor multiplication is {\em computable}, but that both operations are {\em weakly computable}; we introduce both kinds of computability in greater generality. We determine which additive and multiplicative shifts (restrictions of addition and multiplication to one variable) are computable, and prove that each of these shifts becomes computable after a~permutation of encoding. We ask if it is the case for the bivariate addition and multiplication.
Keywords
Cite
@article{arxiv.2108.02046,
title = {Rethinking real numbers as infinite decimals},
author = {Martin Klazar},
journal= {arXiv preprint arXiv:2108.02046},
year = {2021}
}
Comments
After arXiv:0910.5870 in 2009 this is my another, hopefully better, attempt to treat infinite decimal expansions