An Unusual Proof that the Reals are Uncountable

TL;DR

This paper presents a unique proof that the set of real numbers is uncountable, adapted from Bourbaki's work, offering an alternative perspective on a classical mathematical fact.

Contribution

It introduces an unusual proof method for the uncountability of reals, differing from standard proofs and inspired by Bourbaki's approach.

Findings

The proof confirms the uncountability of reals using a novel approach.

It provides an alternative perspective to classical proofs.

The method may inspire new ways to understand uncountability.

Abstract

This somewhat unusual proof for the fact that the reals are uncountable, which is adapted from one of Bourbaki's proofs in "Fonctions d'une variable reelle", may be of some interest.