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Re: Dear Nico B. (Not Benschop) & 5 BSM
Posted:
May 23, 2000 11:40 PM
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denis-feldmann wrote:
> Pertti Lounesto <Pertti.Lounesto@hit.fi> a ÃÂécrit:
> > Jan Stevens wrote:
> >
> > > Pertti Lounesto <Pertti.Lounesto@hit.fi> writes:
> > > >> > Jan Stevens wrote:
> > > >> >> Pertti Lounesto <lounesto@pop.hit.fi> writes:
> > > >> >>>
> > > >> >>> Dear Nicolas Bourbaki,
> > > >> >>>
> > > >> >>> I think that your Lemme 5, on page 151, of
> > > >> >>>
> > > >> >>> N. Bourbaki: Alg\`ebre, Chapitre 9, Formes
> > > >> >>>sesquilin\'eaires et formes quadratiques,
> > > >> >>>Hermann, Paris, 1959,
> > > >> >>>
> > > >> >>>does not hold. For a counterexample, consult
> > > >> >>>
> > > >> >>>http://www.hit.fi/~lounesto/counterexamples.htm.
> > >
> > > It would be really helpful for readers of Bourbaki if
> > > Lounesto pointed out which step of the proof in the
> > > original version is wrong. After all the case distinction
> > > dim E even or odd is made there.
> >
> > Bourbaki's mistake has been regarded significant enough
> > to comment by Deheuvels 1981, p. 355 and Moresi 1988,
> > p. 621, in
> >
> > R. Deheuvels: Formes quadratiques et groupes classiques,
> > Presses Universitaires de France, Paris, 1981, and
> >
> > R. Moresi: A remark on the Clifford group of a quadratic
> > form; pp. 621-626 in Stochastic Processes, Physics and
> > Geometry, Ascona/Locarno, 1988.
> >
> > As for locating the erroneous step of the proofs, I have
> > never commented on that, because the validity of a
> > counterexample to a theorem/lemma does not depend on
> > its proof.
>
> Interesting remark; showing a lot on your general mathematical abilities
Since you are so good in locating erroneous steps in
proofs, and in evaluating my mathematical abilities, why
don't you locate a possible error in my proof presented
in http://www.hit.fi/~lounesto/Robin.Chapman (to a
theorem, which I was challenged to prove)?
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