KANTOR Georg (Cantor Georg)( German mathematician.)
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Biography KANTOR Georg (Cantor Georg)
Born March 3, 1845 in St. Petersburg. Educated at the universities of Zurich, Berlin and GцTttingen. At the age of 24 became a privat-docent in 1872 - Adjunct Professor, in 1879 - professor of mathematics at the University of Gaul.
The first work devoted to Cantor trigonometric series (Fourier series). During these studies he created the theory of irrational numbers, which received wide recognition. In 1874, proved that the set of all real numbers is uncountable, in 1878 formulated the concept of power set. In the works of 1879-1884 demonstrated the principles of his teaching concerning the infinity, . based on the concept of 'significant difference between the concepts of potential and actual infinity, . the first of which means a variable final value of, . increase indefinitely, . whereas the second - fixed, . constant value, . which surpasses all finite values',
. Based on the concept of actual infinity, Cantor constructed a theory of transfinite cardinal numbers, and presented it in the basis of general theory of manifolds (Grundlagen einer allgemeinen Mannigfaltigkeitslehre, 1883). The lower cardinal number attributed to a countable set higher - a continuum. This created the arithmetic of transfinite numbers, similar to the usual arithmetic. Kantor also gave a definition of transfinite ordinal numbers. Kantor died in Halle on Jan. 6, 1918.