SET THEORY

CANTOR, G.

Fondements d'une théorie générale des ensembles (+) Sur divers théorémes de la théorie des ensembles de points situs - dans un espace continu a n dimensions.

[Berlin, Stockholm, Paris, F. & G. Beijer, 1883]. 4to. Without wrappers as extracted from "Acta Mathematica. Hrdg. von G. Mittag-Leffler.", Bd. 2. Fine and clean. Pp. 381-414.

First French translation (and translation in general) of Cantor's fifth, thus most important, paper in his series of papers which founded set theory. (The first mentioned).

It contained Cantor's reply to the criticism of the first four papers and showed how the transfinite numbers were a systematic extension of the natural numbers. It begins by defining well-ordered sets. Ordinal numbers are then introduced as the order types of well-ordered sets. Cantor then defines the addition and multiplication of the cardinal and ordinal numbers. In 1885, Cantor extended his theory of order types so that the ordinal numbers simply became a special case of order types. It was later published as a separate monograph.

The concept of the existence of an infinity was an important shared concern within the realms of mathematics, philosophy and religion. Preserving the orthodoxy of the relationship between God and mathematics was long a concern of Cantor's. He directly addressed this relationship between these disciplines in the introduction to the present paper, where he stressed the connection between his view of the infinite and the philosophical one. To Cantor, his mathematical views were closely linked to their philosophical and theological implications-he identified the Absolute Infinite with God and he considered his work on transfinite numbers to have been directly communicated to him by God, who had chosen Cantor to reveal them to the world.

Order-nr.: 45855