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PP-1788:
The voting period herewith
begins. Voting will continue until after Wednesday, June 6, 2012.
Voting on this motion will proceed according to the rules for
position papers (quorum and simple majority).
Comment can continue during voting, but the motion
cannot be changed during voting.
Juergen: Please update the web page with this action.
Acting secretary: Please record the transaction in the minutes.
The motion appears in the private area of the IEEE P-1788 site:
http://grouper.ieee.org/groups/1788/private/Motions/AllMotions.html
I have also attached the motion, for your convenience.
As usual, please contact me if you need the password to the private
area.
Note that there are now TWO motions under vote: 33 and 34.
Best regards,
Baker (acting as chair, P-1788)
P.S. I apologize for the delay in bringing this motion to a vote.
I take full responsibility.
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
--
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
-- --------------------------------------------------------------- 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 ---------------------------------------------------------------
Attachment:
Motion.pdf
Description: Adobe PDF document