Cantor's theorem: Difference between revisions

Revision as of 16:13, 8 December 2003

Revision as of 21:07, 27 January 2004

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== History ==

Though it is called "Cantor's Theorem", Cantor never gave a proof in precisely this form. His first proof of the non-denumerability of the reals was was written in 1873 and published in 1874 (see [[Cantor's first uncountability proof]]). This does not resemble the theorem at all.

In a famous paper published in 1891 ("Ueber eine elementare Frage der Mannigfaltigkeitslehre"), where the diagonal proof first appears, there is a another proof later in this paper, where he notes that if ''f'' is a function defined on ''X'' whose values are 2-valued functions on ''X'', then the 2-valued function ''G''(''x'') = 1 − ''f''(''x'')(''x'') is not in the range of f.