Sv: Do I have a second? Re: Notations, new Motion
Yes, I second this motion.
Best wishes,
Bo
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Bo Einarsson
Ekholmsvägen 249
SE-589 29 LINKÖPING
SWEDEN
Tel 013 - 151896
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----Ursprungligt meddelande----
Från: rbk@xxxxxxxxxxxxx
Datum: 2012-04-16 17:23
Till: "Ulrich Kulisch"<Ulrich.Kulisch@xxxxxxxxxxx>
Kopia: "stds-1788"<stds-1788@xxxxxxxxxxxxxxxxx>
Ärende: Do I have a second? Re: Notations, new Motion
P-1788,
Do I have a second for this motion?
Baker
On 04/16/2012 10:13 AM, Ulrich Kulisch wrote:
> The text of a new Motion is attached. The following mail exchange
gives the rationale.
>
> Best regards
> Ulrich
>
>
>
> On March 26, 2012 Ulrich Kulisch wrote:
>
> Dear all,
>
> There are some discrepancies in the notations of Drafts 4.02 and 4.04
and I think
> we should straighten these out before less suited denotations spread.
Let me briefly
> comment on the history of these notations.
> The real numbers R are defined as conditionally complete, linearly
ordered field.
> Conditionally complete means: Every bounded subset has an infimum and
a supremum.
> Every conditionally completely ordered set can be completed by
joining a least and a
> greatest element. In case of the real numbers R these are ?? and +?.
However, these
> new elements are not real numbers. For instance ??? not= 0, or ?/?
not= 1. I think
> there was general agreement that the completion should be expressed
by overlining the
> R. So \overline{R} := R ? {??,+?}.
> Since the early days of interval arithmetic the set of nonempty,
closed and bounded
> real intervals has been denoted by IR. The ordering of the set {IR,
?} also is only
> conditionally complete. For every bounded subset the infimum is the
intersection and
> the supremum is the interval hull. Completion of {IR, ?} brings the
empty set and
> unbounded intervals into the game. In my book (2008) and in the paper
I prepared
> for the proceedings of the Dagstuhl meeting (January 2008) I denoted
the completed
> set by (IR). This was critisized within P1788. Then I suggested
writing JR for the
> completed set. After some discussion I think we all agreed indicating
the completion
> again by overlining the set IR. In \overline{IR} the empty set is the
least element. However, the empty set is not an interval
arithmetically. As ?? and +? are not real numbers the empty set does
not follow conventional rules of interval
> arithmetic, for instance, ? · 0 not= 0.
> For consistency the same scheme of denotations should be kept for the
subsets
> representable on computers. This leads to the following denotations:
> R the set of real numbers.
> \overline{R} \overline{R} := R ? {??,+?}.
> IR the set of nonempty, closed and bounded real
intervals.
> \overline{IR} the set of closed real intervals, including unbounded
intervals and the empty set.
> F the set of (finite) floating-point numbers
representable in some floating-point format.
> \overline{F} \overline{F} := F ? {??,+?}.
> IF the intervals of IR whose bounds are in F.
> \overline{IF} the intervals of \overline{IR} whose bounds are in
\overline{F} and the empty set.
>
> Best regards
> Ulrich
>
> On April 4, 2012 Ralph Baker Kearfott wrote:
>
> Ulrich et al:
>
> We can take your notaional comments into consideration when writing
the actual standard text. Also, it is in general a good idea to use our
agreed upon notation in position papers. However, I view motion 31, as
a position paper, as
> providing guidance for actual writing the standard text, so the
meaning in motion 31 is what is of primary importance. That is, even
when Motion 31 passes, we can still use your notation in the text.
>
> Best regards, Baker
>
> On April 4, 2012 Ulrich Kulisch wrote:
>
> Baker,
>
> it is not my notation. I think about two years ago we agreed upon the
notation. I believe it is important that we settle this question now
and not at the end of the standardization process. Many of us are still
writing papers and even books
> on interval arithmetic and on applications. Standardizing the
denotation of basic concepts is an essential contribution to the
understanding and communication within P1788 and in the interval
community.
> If Motion 31 passes I really do not know which notation I should use
in a paper I just have under preparation.
>
> Should there still be disagreement upon the notation of the basic
sets we should settle the question by another motion.
>
> Best regards
> Ulrich
>
>
> --
> Karlsruher Institut für Technologie (KIT)
> Institut für Angewandte und Numerische Mathematik (IANM2)
> D-76128 Karlsruhe, Germany
> Prof. Ulrich Kulisch
>
> Telefon: +49 721 608-42680
> Fax: +49 721 608-46679
> E-Mail:ulrich.kulisch@xxxxxxx
> www.kit.edu
> www.math.kit.edu/ianm2/~kulisch/
>
> KIT - Universität des Landes Baden-Württemberg und nationales
Großforschungszentrum in der Helmholtz-Gemeinschaft
>
>
--
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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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