Georg Cantor


Also found in: Dictionary, Thesaurus, Medical, Wikipedia.

Cantor, Georg

(gā`ôrkh kän`tôr), 1845–1918, German mathematician, b. St. Petersburg. He studied under Karl Weierstrass and taught (1869–1913) at the Univ. of Halle. He is known for his work on transfinite numbers and on the development of set theory, which is the basis of modern analysis, as well as for his definition of irrational numbers. His approach to the concept of the infinite revolutionized mathematics by challenging the processes of deductive reasoning and led to a critical investigation of the foundations of mathematics.

Cantor, Georg

 

Born Mar. 3, 1845, in St. Petersburg; died Jan. 6, 1918, in Halle. German mathematician.

Cantor graduated from the University of Berlin in 1867. He developed the theory of infinite sets and the theory of transfinite numbers. In 1874 he proved the uncountability of the set of all real numbers, thus establishing the existence of inequivalent (that is, having different powers) infinite sets; he formulated (1878) the general concept of the power of a set. Between 1879 and 1884, Cantor systematically set forth the principles of his study of infinity. He introduced the concepts of limit point and derived set, constructed an example of a perfect set, developed one of the theories of irrational numbers, and formulated one of the axioms of continuity. In 1897 he retired from scientific work. Cantor’s ideas encountered intense opposition from his contemporaries, in particular from L. Kronecker, but they subsequently exerted great influence on the development of mathematics.

WORKS

Gesammelte Abhandlungen mathematischen und philosophischen Inhalts Berlin, 1932.
In Russian translation:
“Uchenie o mnozhestvakh.” In the collection Novye idei v matematike, no. 6. St. Petersburg, 1914.
References in periodicals archive ?
19) Juan Antonio Hernandez, "Biografia del infinito: La nocion de transfinitud en Georg Cantor y su presencia en la prosa de Jorge Luis Borges", Signos: Literarios y Linguisticos, 2.
2) Georg Cantor, "Ober unendliche, lineare Punktmannichfaltigkeiten Nr.
Possible reasons for Cantor's switch from the generative concept of ordinal numbers--in spite of its philosophical advantage (for example, in connection with the paradoxes) of highlighting the open-endedness inherent in the progression of transfinite numbers--to the "purely mathematical" treatment of order types of well-orders may be gleaned from his letters to Mittag-Leffler of September 23, 1883 and to Labwitz of February 15, 1884, see Georg Cantor Briefe, ed.
10) Georg Cantor, "Principien einer Theorie der Ordnungstypen.
12) For the purpose of illustration see the hypothesis about the cardinalities of the set of corporeal monads and the set of ether monads put forward in the closing remarks of Georg Cantor, "Uber verschiedene Theoreme aus der Theorie der Punktmengen in einem n-fach ausgedehnten, stetigen Raume [G.
See Georg Cantor "Uber unendliche, lineare Punktmannichfaltigkeiten Nr.
The first appearance of [epsilon]-numbers is in Georg Cantor, "Beitrage zur Begrundung der transfiniten Mengenlehre," Mathematische Annalen 49 (1897): [section]20; Ges.
We mean here the problem in its original formulation in Georg Cantor,