Tav (number)
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In his work on set theory, Georg Cantor denoted the collection of all cardinal numbers by the last letter of the Hebrew alphabet, 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.[1],[2]
[edit] References
- ^ 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, dated July 28, 1899. However, as Ivor Grattan-Guinness has discovered[4], 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.
- ^ 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.
- ^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.
- ^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.
