Signed-Bit Representations of Real Numbers
Logic
2015-10-05 v1
Abstract
The signed-bit representation of real numbers is like the binary representation, but in addition to 0 and 1 you can also use -1. It lends itself especially well to the constructive (intuitionistic) theory of the real numbers. The first part of the paper develops and studies the signed-bit equivalents of three common notions of a real number: Dedekind cuts, Cauchy sequences, and regular sequences. This theory is then applied to homomorphisms of Riesz spaces into the reals.
Cite
@article{arxiv.1510.00648,
title = {Signed-Bit Representations of Real Numbers},
author = {Robert Lubarsky and Fred Richman},
journal= {arXiv preprint arXiv:1510.00648},
year = {2015}
}