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Discussion period for Motions 25 and 26 extended Re: KISS-decorations



P-1788,

Since Motions 25, 26, and 27 present three alternatives for decorations,
it is appropriate that they be discussed together.  Thus, unless I
receive objections, the discussion periods for motions 25 and 26 are
herewith extended to after July 26, to correspond to the discussion
period for Motion 27.  Please study and discuss!

Baker

On 6/29/2011 12:56 AM, John Pryce wrote:
Marco, Jürgen, P1788

On 28 Jun 2011, at 21:13, Jürgen Wolff von Gudenberg wrote:
we have prepared a third motion on decorations that clearly follows the KISS principle. Perhaps  it is too simple, but we are convinced that it works better than the two current approaches. We only have 4 different decorations and one linear order.
We are eager to read your comments.
Perhaps we can prolong the discussion time again? but there is not much discussion(!)

Thank you. I like the push back towards simplicity. Arnold has more-or-less completed his new FTDIA proof and has sent me a part for checking. I think we both want to revert from the present 7-decoration idea, and get rid of boundedness. Yes, please chairman, can we extend the discussion period?

That said, I have some criticisms.

1. Theorem 1 on p2 is surely well known to be false.
    Let f(x)=x for real x. Define F: IR ->  IR by
       F(xx) = Entire if 0 not in xx, and xx otherwise.
    Then for any xx, and x in xx, we have f(x) in F(xx), so F
    is an interval extension of f.
    But xx=[1,2], yy=[0,2] give F(xx)=Entire, F(yy)=[0,2], so
    isotonicity fails.

2. Theorem 2 (1st part) is carelessly stated, in fact meaningless as
    written IMO.
    It's not "For every interval extension F ...", but "For the
    particular interval *function* F that results from applying straight-
    forward interval computation ..., F(xx) encloses the range of f
    over xx" -- or better, "... encloses the range over xx of the point
    function defined by the expression f."

3. And surely Theorem 2 (2nd part) needs some continuity assumption,
    because of the effect of taking the hull. I think it's false for
    f(x)=1/x with xx=[-1,1]. And for sign(x) with xx=[0,0.5].

Further, and I trust more constructive, remarks to follow.

John



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Ralph Baker Kearfott,   rbk@xxxxxxxxxxxxx   (337) 482-5346 (fax)
(337) 482-5270 (work)                     (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
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