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Topic: Only for mathematicians!
Replies: 5   Last Post: Aug 16, 2014 3:48 PM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Only for mathematicians!
Posted: Aug 16, 2014 12:33 PM

On Saturday, 16 August 2014 18:20:43 UTC+2, Ben Bacarisse wrote:

> It's all about words. Prof. Mueckenhiem's mathematicc
> is the same as everyone else's. He *thinks* there's a difference,

Should we briefly characterize the new view of the infinite introcued by Cantor, we could certainly say: In analysis we have to deal only with the infinitely small and the infinitely large as a limit-notion, as something becoming, arising, being under construction, i.e., as we put it, with the potential infinite. But this is not the proper infinite. This we have for instance when we consider the entirety of the numbers 1, 2, 3, 4, ... itself as a completed unit, or the points of a length as an entirety of things which is completely available. This sort of infinity is named actual infinite.
[David Hilbert: "Über das Unendliche", Mathematische Annalen 95 (1926) p. 167]

In spite of significant differences between the notions of the potential and actual infinite, where the first is a variable finite magnitude, growing above all limits, the latter a quantity fixed in itself but beyond all finite magnitudes, it happens deplorably frequently that the one is confused with the other.
[...] improper infinite = variable finite = syncategorematice infinitum on the one side and proper infinite = transfinitum = completed infinite = being infinite = categorematice infinitum on the other [...]
[E. Zermelo: "Georg Cantor, Gesammelte Abhandlungen mathematischen und philosophischen Inhalts", Springer (1932)]

Regards, WM

Date Subject Author
8/16/14 Ben Bacarisse
8/16/14 mueckenh@rz.fh-augsburg.de
8/16/14 Virgil
8/16/14 Ben Bacarisse