The Continuum is Countable: Infinity is Unique

TL;DR

This paper claims to prove that the set of real numbers has the same cardinality as the set of integers, challenging established set theory and the continuum hypothesis, and suggests a single dimension for infinite sets.

Contribution

It presents a novel proof that the continuum is countable and argues for a unique dimension for all infinite sets, contradicting classical results.

Findings

The set of real numbers has the same cardinality as the set of integers.

There is only one dimension for infinite sets, Aleph.

The continuum hypothesis is challenged by this proof.

Abstract

Since the theory developed by Georg Cantor, mathematicians have taken a sharp interest in the sizes of infinite sets. We know that the set of integers is infinitely countable and that its cardinality is Aleph0. Cantor proved in 1891 with the diagonal argument that the set of real numbers is uncountable and that there cannot be any bijection between integers and real numbers. Cantor states in particular the Continuum Hypothesis. In this paper, I show that the cardinality of the set of real numbers is the same as the set of integers. I show also that there is only one dimension for infinite sets, Aleph.