Re: Ullrich the Mathematician!

From: The World Wide Wade (waderameyxiii_at_comcast.remove13.net)
Date: 03/10/05 

Date: Thu, 10 Mar 2005 09:55:38 -0800

In article <k0m0315v8re5u5rcedsuvheu6m68mctest@4ax.com>,
 David C. Ullrich <ullrich@math.okstate.edu> wrote:

> >[snip of example]:
> >
> >This is perhaps simpler, and has the virtue of giving
> >differentiability everywhere on [0,1]: [..]
> >
> >So Gabriel fails rather badly here, even though f is
> >differentiable everywhere on [0,1]. The problem comes from the
> >wildness of f'. A natural remedy is to assume f' is continuous on
> >[0,1], but as noted a billion times already, the result is then a
> >trivial consequence of FTC. In summary, when Gabriel is of
> >interest, it's false. When it's true, it's of no interest.
>
> Yes, that is probably simpler.
>
> Had you pointed out an example like this previously?
> (Not worried about copyright or anything, just wondering
> whether I missed something - I've been telling people that
> the theorem seems pretty likely false but that nobody'd
> given an actual counterexample.)

No I hadn't. I saw that example in Stromberg had come up again,
and while it's nice (assuming it works, has anyone gone through
it?), I started looking for a simpler counterexample wrt Gabriel.

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