HMC real numbers in Countable Mathematical Analysis

2023/08/08 by Martin Klazar, Klazar, Martin
Computer Science · Mathematics · #26A03 #Computability, Logic, AI Algorithms #FOS: Mathematics #History and Overview (math.HO) #Logic (math.LO) #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2308.04474

openalex publication_date 2023/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a theory of real numbers as rational Cauchy sequences, in which any two of them, (a_n) and (b_n), are equal iff lim (a_n-b_n)=0. We need such reals in the Countable Mathematical Analysis ([4]) which allows to use only hereditarily at most countable (HMC) sets.

Related

• Countable real analysis
• The reals as rational Cauchy filters
• Countability of the Real Numbers
• The property of the set of the real numbers generated by a Gelfond-Schneider operator and the countability of all real numbers
• Counting the Positive Rationals: A Brief Survey