The trigonometric background to Georg Cantor's theory of sets

1 Cantor's papers on the theory of sets and transfinite numbers have been most widely popularized by the writings of P. E. B. Jourdain, and in particular through his translation, Georg Cantor: Contributions to the Founding of the Theory of Transfinite Numbers, trans: Jourdain (Chicago, 191 5 ; Dover reprint: New York, 1955). Despite Jourdain' s occasionally torturous rendering of the German into English, his introduction manages to describe the context and development of Cantor's mathematical work, though Jourdain says little about the papers on trigonometric series. A more detailed account of Cantor's mathematical corpus is given by Jourdain in a series of articles: "The Development of the Theory of Transfinite Numbers," Archiv der Mathematik und Physik (Grunert's Archiv), 10 (1906) 254-281; 14 (1909) 289-311; 16 (1910) 21-43; 22 (1913) 1-21. For details on the significance and interpretation of Cantor's continuum hypothesis consult Kurt Godel: "What is Cantor's Continuum Problem ?" American Mathematical Monthly, 542 (1947) 515-525. Godel's paper is reprinted in a revised and expanded version in P. Benacerraf & H. Putnam, eds. : Philosophy of Mathematics, Selected Readings (New Jersey, 1964).