Motion P1788/M0002.01_ProcessStructure NO
YES
Having read the position paper again I think thefact that
the \curly{I} operator is not specified allows for the definition of
all kinds of intervals
1. bounded closed connected sets of reals (Moore)
2. closed connected sets of reals (Vienna proposal and Kulisch)
3. closed connected subsets of extended reals
4. extended intervals (modal or Kaucher)
5. wraparound intervals (Kahan).
Jürgen Wolff v Gudenberg
I would vote YES if we add the sentence
The \curly{I} operator denotes a manner to define intervals over a set S
either by building pairs [s1,s2] with s1,s2 \in S and s1<=s2
or by building pairs [s1,s2] with s1,s2 \in S or pairs [-infty,s2] or
pairs [s1, and s1<=s2
In table 2 the underlying number system \curly{R} and intervals built
from this \curly{IR} is found
The \curly{I} operator is not defined, hence implicitly, I assume it is
by building pairs. We should allow for more flexibility here, as is done
in Kulisch's Dagstuhl publication.
The current text of the position paper suggests the following options
1. if \curly{R} = \R \IR means the set of all bounded closed
intervals
2. if \curly{R} = \R* = \R u {-infty,+infty}
\IR* = *\IR (see notation paper) means the set of all bounded
closed intervals over \R*, i.e. +- infty may be member of an
interval
Kulisch proposes:
3. (IR) denoting the set of all closed and connected intervals
if bounds are infinite, they do not belong to the interval,
hence [infty, infty] is not possible
On the other hand we could propose
4. IR to be the same set as in 2. but without infinite point
intervals.
I propose to amend the motion by adding the specification of the
\curly{I} operator.
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