Countable real analysis

2023/01/17 by Klazar, Martin
#26A06 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #History and Overview (math.HO) #Logic (math.LO) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2301.08142

Abstract

HMC sets are hereditarily at most countable sets. We rework a substantial part of univariate real analysis in a form in which only HMC real functions are used. In such countable real analysis we carry out Hilbert's proof of transcendence of the number e. We also construct a uniformly continuous function f:[0,1]∩ℚ→ℝ such that f'=1 on [0,1]∩ℚ and lim_\substacka→1/√(2) a∈ℚf(a)=(1)/(√(2))>f(b) for every b∈[0,1]∩ℚ.

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