FIRST CONTRIBUTION TO SET THEORY AND THE BIRTH OF THE THEORY OF THE TRANSFINITE

CANTOR, G.

Sur une propriété du systéme de tous les nombres algébriques réels. [Translated from the German: Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen].

[Berlin, Stockholm, Paris, F. & G. Beijer, 1883]. 4to. Without wrappers as extracted from "Acta Mathematica. Hrsg. von G. Mittag-Leffler.", Bd. 2. Fine and clean. Pp. 305-328.

First French [and general] translation of Cantor's famous and exceedingly influential paper which contains the first proof that the set of all real numbers is uncountable; also contains a proof that the set of algebraic numbers is denumerable. "This article is Cantor's first published contribution to the theory of sets. The deep and epoch-making result of the paper is not the easy theorem alluded to in the title - the theorem that that the class of real algebraic numbers is countable - but rather the proof, in §2, that the class of real numbers is not countable [...]. And that marks the start of the theory of the transfinite. [Ewald, Pp. 839-40].

"The first published writing on set theory [the present paper], contained more than the title indicated, including not only the theorem on algebraic numbers but also the one on real numbers, in Dedekind's simplified version, which differs from the present version in that today we use the "diagonal process," then unknown" (DSB)

Order-nr.: 45857