Dieudonne on Dedekind

[Colin McLarty]

He may have said this.  But what I know he said is that Dedekind reals were
useless, compared to the axiomatic definition of the reals as a complete
ordered field, for students before the "troisieme cycle d'university."   I
am not sure exactly what that meant in France in 1974, but it seems to have
meant something like graduate students.

This is from "Devons-nous enseigner les " mathématiques modernes " ?" Jean
A. Dieudonné, Bulletin de l’APMEP n° 292 de février 1974  on line at

 http://michel.delord.free.fr/dieudonne-1974.html

Ces applications, cependant, sont bien au-dessus du niveau de l'étudiant
> avant le troisième cycle des universités, et je partage l'opinion de Thom
> que les "coupures" traditionnelles de Dedekind ou les façons analogues de
> "définir" des nombres réels sont parfaitement inutiles et même nuisibles à
> ce niveau. ...  Mais je pense qu'il ne peut être que profitable à
> l'étudiant de posséder une liste précise des propriétés fondamentales des
> nombres réels qu'il utilisera constamment en analyse et c'est ce que l'on
> appelle un "système d'axiomes des nombres réels"


Colin


On Mon, Aug 9, 2021 at 2:52 PM James Robert Brown <jrbrown at chass.utoronto.ca>
wrote:

>
> Several years ago I read something by Jean Dieudonne where he said
> (perhaps only in passing) that he wanted to reject Dedekind’s theory of
> real numbers because it was fruitless; it was not generating any new
> research.
>
> Does anyone know of an article by him (or anyone else) along this line?
>
> Many thanks,
>
> Jim
>
>
> *************************
> James Robert Brown
> Professor Emeritus
> Department of Philosophy
> University of Toronto
> Toronto  M5R 2M8
> Canada
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