Dieudonne on Dedekind

[Hendrik Boom]

On Mon, Aug 09, 2021 at 03:43:43PM -0400, Colin McLarty wrote:
> 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.

Both my wife and I took "Basic Concepts of Mathematical Analysis"
in the first year of the honours mathematics program at 
the university of Manitoba in th 1960's.

But we entered the program at different times, and got it taught in 
different ways.

I got the axiomatic definition of the reals as a coplete ordered field.

She got the construction of the reals out of the integers.  I don't know 
whether the reals were made out of Cauchy sequences or out of Dedekind 
cuts.

The course I got was clear and comprehensible.
The course she got turned her away from mathematics.

I don't know if this is the kind of reason Dieudonné considered the 
approach useless ... 

-- hendrik
  
> 
> 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
> > Home: 519-439-2889, Cell: 519-854-0131
> > Philosophy Dept. page:
> > http://www.philosophy.utoronto.ca/directory/james-robert-brown/
> > Home page: http://www.chass.utoronto.ca/~jrbrown/index.html
> >
> >
> >
> >
> >
> >