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Topic: [HM] Cantor's diagonal proof
Replies: 14   Last Post: Mar 21, 2004 12:28 PM

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Julio Gonzalez Cabillon

Posts: 1,353
Registered: 12/3/04
Re: [HM] Cantor's diagonal proof
Posted: Mar 21, 2004 12:28 PM
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On Mar 1, 2004, at 1:37 AM, Thierry Guitard wrote:

<< the diagonal trick was used by Du Bois Reymond twenty years before
Cantor to prove there is no universal criterium of convergence ! It
is well documented in the paper of Fisher on DBR in AHES. >>

and Bill Tait replied:

<< As far as I know, Hao Wang, in _From Mathematics to Philosophy_
(1974), was first to suggest that the idea of Cantor's argument was
anticipated by DBR. But I question his opinion. Since I don't know
what 'AHES' stands for nor which Fisher wrote the paper, I haven't
been able to follow up Thierry Guitard's reference. >>

1. Most probably, the paper alluded by Thierry is Gordon Fisher's
excellent "The Infinite and Infinitesimal Quantities of du Bois-
Reymond and their Reception", _Archive for the History of Exact
Sciences_, vol 24 (1981), pp. 101-163.

2. Dirk van Dalen and A.F. Monna, in their "Sets and Integration: An
Outline of the Development" (Groningen, 1972), already suggested the
idea of that Cantor's argument was anticipated by DBR, and I suspect
that this might have been remarked earlier (than 1972).

Best wishes, Julio.

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