- Tav (number)
In his work on
set theory ,Georg Cantor denoted the collection of allcardinal number s by the last letter of the Hebrewalphabet , Ivrit|ת (transliterated as Taf, Tav, or Taw.) As Cantor realized, this collection could not itself have a cardinality, as this would lead to a paradox of the Burali-Forti type. Cantor instead said that it was an "inconsistent" collection which was absolutely infinite. ["Gesammelte Abhandlungen"3, Georg Cantor, ed. Ernst Zermelo, Hildesheim: Georg Olms Verlagsbuchhandlung, 1962, pp. 443–447; translated into English in "From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931", ed. Jean van Heijenoort, Cambridge, Massachusetts: Harvard University Press, 1967, pp. 113–117. These references both purport to be a letter from Cantor to Dedekind, datedJuly 28 ,1899 . However, asIvor Grattan-Guinness has discovered4, this is in fact an amalgamation by Cantor's editor,Ernst Zermelo , of two letters from Cantor to Dedekind, the first dated July 28 and the second dated August 3.] , [ [http://www.digizeitschriften.de/home/services/pdfterms/?ID=516934 The Correspondence between Georg Cantor and Philip Jourdain] , I. Grattan-Guinness, "Jahresbericht der Deutschen Mathematiker-Vereinigung" 73 (1971/72), pp. 111–130, at pp. 116–117. ]References
- ^"Gesammelte Abhandlungen mathematischen und philosophischen Inhalts", Georg Cantor, ed. Ernst Zermelo, with biography by Adolf Fraenkel; orig. pub. Berlin: Verlag von Julius Springer, 1932; reprinted Hildesheim: Georg Olms, 1962, and Berlin: Springer-Verlag, 1980, ISBN 3540098496.
- ^ [http://www.digizeitschriften.de/home/services/pdfterms/?ID=516899 The Rediscovery of the Cantor-Dedekind Correspondence] , I. Grattan-Guinness, "Jahresbericht der Deutschen Mathematiker-Vereinigung" 76 (1974/75), pp. 104–139, at p. 126 ff.
See also
*
Aleph number
*Absolute Infinite
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