Countable real analysis

Martin Klazar

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arXiv · 2301.08142

Countable real analysis

Martin Klazar

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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 $\mathrm{e}$. We also construct a uniformly continuous function $f:[0,1]\cap\mathbb{Q}\to\mathbb{R}$ such that $f'=1$ on $[0,1]\cap\mathbb{Q}$ and $\lim_{\substack{a\to1/\sqrt{2}\\a\in\mathbb{Q}}}f(a)=\frac{1}{\sqrt{2}}>f(b)$ for every $b\in[0,1]\cap\mathbb{Q}$.

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BibTeX RIS

Martin Klazar. 2023-01-17. Countable real analysis. https://arxiv.org/abs/2301.08142

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