Tav (number): Difference between revisions
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{{short description|Representation of the collection of all cardinal numbers}} |
{{short description|Representation of the collection of all cardinal numbers}} |
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In his work on [[set theory]], [[Georg Cantor]] denoted the collection of all [[cardinal number]]s by the last letter of the [[Hebrew alphabet]], '''{{lang|he|ת}}''' (transliterated as '''Tav''', '''Taw''', or '''Sav'''.) As Cantor realized, this collection could not itself have a cardinality, as this would lead to a paradox of the [[Burali-Forti paradox|Burali-Forti]] type. Cantor instead said that it was an "inconsistent" collection which was [[Absolute |
In his work on [[set theory]], [[Georg Cantor]] denoted the collection of all [[cardinal number]]s by the last letter of the [[Hebrew alphabet]], '''{{lang|he|ת}}''' (transliterated as '''Tav''', '''Taw''', or '''Sav'''.) As Cantor realized, this collection could not itself have a cardinality, as this would lead to a paradox of the [[Burali-Forti paradox|Burali-Forti]] type. Cantor instead said that it was an "inconsistent" collection which was [[Absolute infinite|absolutely infinite]].{{#tag:ref|''Gesammelte Abhandlungen'',<ref>''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|3-540-09849-6}}.</ref> 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 [[Richard Dedekind|Dedekind]], dated July 28, 1899. However, as [[Ivor Grattan-Guinness]] has discovered,<ref>[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.</ref> 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.|name=GesammelteAbhandlungen}}<ref>[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.</ref> |
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== See also == |
== See also == |
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* [[Taw (letter)]] |
* [[Taw (letter)]] |
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* [[Aleph number]] |
* [[Aleph number]] |
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* [[Absolute |
* [[Absolute infinite]] |
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==References== |
==References== |
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Latest revision as of 06:35, 23 May 2024
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 Tav, Taw, or Sav.) 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.[3][4]
See also
[edit]References
[edit]- ^ 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 3-540-09849-6.
- ^ 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.
- ^ Gesammelte Abhandlungen,[1] 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,[2] 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.
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