Une initiation au concept de l'infini

Fuente: arXiv
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Autori principali: Ades, Michel, Guillemette, David, Provost, Serge B.
Natura: Preprint
Pubblicazione: 2024
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author Ades, Michel
Guillemette, David
Provost, Serge B.
author_facet Ades, Michel
Guillemette, David
Provost, Serge B.
contents In this article, we explore the notion of infinity by studying Cantor's contribution to this field. A brief history of set theory is given. As an example of infinity, we consider Hilbert's famous hotel. A graphical construction is used to demonstrate the countability of rationals. Cantor's diagonal procedure is explored, demonstrating that the infinity of real numbers is greater than that of integers. There is therefore a hierarchy of infinities, enabling us to elaborate on the continuum hypothesis, which remains an unsolved problem in mathematics.
format Preprint
id arxiv_https___arxiv_org_abs_2403_12067
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Une initiation au concept de l'infini
Ades, Michel
Guillemette, David
Provost, Serge B.
History and Overview
11-xx:Number theory, 11-01, 11-02, 11-03
In this article, we explore the notion of infinity by studying Cantor's contribution to this field. A brief history of set theory is given. As an example of infinity, we consider Hilbert's famous hotel. A graphical construction is used to demonstrate the countability of rationals. Cantor's diagonal procedure is explored, demonstrating that the infinity of real numbers is greater than that of integers. There is therefore a hierarchy of infinities, enabling us to elaborate on the continuum hypothesis, which remains an unsolved problem in mathematics.
title Une initiation au concept de l'infini
topic History and Overview
11-xx:Number theory, 11-01, 11-02, 11-03
url https://arxiv.org/abs/2403.12067