A new approach to the real numbers
Liangpan Li

TL;DR
This paper presents a comprehensive approach to defining real numbers using decimal representations, integrating classical constructions like Dedekind cuts and Cauchy sequences within this framework.
Contribution
It introduces a unified method for constructing and understanding real numbers through decimal representations, connecting various classical approaches.
Findings
Provides a complete decimal-based construction of real numbers
Explains Dedekind cuts and Cauchy sequences within the decimal framework
Characterizes real numbers as a complete ordered field
Abstract
In this paper we provide a complete approach to the real numbers via decimal representations. Construction of the real numbers by Dedekind cuts, Cauchy sequences of rational numbers, and the algebraic characterization of the real number system by the concept of complete ordered field are also well explained in the new setting.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComputability, Logic, AI Algorithms · Mathematics and Applications · History and Theory of Mathematics
