Re: David Ullrich and World Wide Wade

From: David C. Ullrich (ullrich_at_math.okstate.edu)
Date: 10/20/04 

Date: Wed, 20 Oct 2004 08:59:38 -0500

On Wed, 20 Oct 2004 08:19:36 -0500, David C. Ullrich
<ullrich@math.okstate.edu> wrote:

Two PS's:

>[...]
>
>The hint was mis-stated, by the way... With the correct
>version of the hint one can give a proof of the
>next inequality that's a little simpler than in the
>pdf (it's the direct proof I mentioned to Wade):
>At points where u < 0, 2A - u > -u = |u|. On the
>other hand, at points where u >= 0 we have u <= A,
>so 2A - u >= 2A - A = A >= u = |u|.
>
>So in any case 2A - u >= |u|, so that
>
> |2A - F| = sqrt((2A - u)^2 + v^2) >= sqrt(u^2 + v^2).
>
>_If_ we define g = F/(2A - F) then this shows that |g| <= 1
>as required.

Note that otoh if g = F/(2A + F) then it's not just
that there's problems with the proof of the main
inequality, in fact simple examples show that |g|
is simply _not_ <= 1. (Didn't mention this until
you showed us the proof because I didn't know
that the proof in the pdf used the "fact" that |g| <= 1...)

Also: when you mention this to the guy make certain
to give proper credit to Wade and me...

>>Thanks for the previous help,
>>Isaac
>>
>
>
>************************
>
>David C. Ullrich

************************

David C. Ullrich

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