Georg Cantor et la découverte des infinis.

Abstract

The great mathematician Georg Cantor (1845-1918) has made the striking discovery that there exist several powers of infinity. How did he arrive to this conclusion? This work is intended to be an historical, mathematical and philosophical introduction to that discovery. Historical, with a brief overview of the paradoxes of infinity before Cantor [I]. Mathematical, with the introduction of the minimal mathematical tools to prepare Cantor's work [II]; the core of the work is in part [III], where the two proofs of the existence of different infinities are presented. The famous diagonal proof is studied in details, with possible objections (for ex. by Wittgenstein). Part [IV] is dedicated to the philosophical aspects of Cantor's views; and part [V] expose the main limits of the original Cantorian set theory, together with an introduction to more modern approaches of the study of infinity.

Date of Award	17 Nov 2003
Original language	French
Supervisor	Jacques Dubucs (Promotor)