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).