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arXiv:1902.07366math.HO

A constructive Knaster-Tarski proof of the uncountability of the reals

Ingo Blechschmidt, Matthias Hutzler

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Abstract

We give an uncountability proof of the reals which relies on their order completeness instead of their sequential completeness. We use neither a form of the axiom of choice nor the law of excluded middle, therefore the proof applies to the MacNeille reals in any flavor of constructive mathematics. The proof leans heavily on Levy's unusual proof of the uncountability of the reals.

arXiv comments
two pages, adapted from Eliahu Levy's proof
Journal reference
DOI
Subjects
math.HOHistory and Overview math.LOLogic

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  1. How many real numbers exist? New proof moves closer to an answer 1 comment

    • You sound like you need to read this [0] answer to the question "Are real numbers countable in constructive mathematics?". > You are using the word "constructive" in an unusual way. It is true that, in ZFC, the set of computable real numbers is countable, but that is not…

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