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Re: Motion 2 amendment and coming motions

Dear Juergen and list members,


Please read the inserted comments


Best regards

Dominique


.J. Wolff v. Gudenberg a écrit :

Dear all,
  I support the structure laid out in the position paper.
I am however not sure how much details are reasonable in levels 3 and 4.
But let us start with level 1
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. 

with this the roadmap for further motions seems to be clear
    - decide on number system
    - decide on \curly{I} operator
    - specify operations
alternative roadmap:
    - decide that intervals are sets
    - decide whether infty may be a member
    - decide on bounds representation.

All the text I wrote does implicitly assume that
low <= up in a (standard) interval [low,up]
Non-standard intervals shall be dealt with later

best regards
Juergen





--
Dr Dominique LOHEZ
ISEN
41, Bd Vauban
F59046 LILLE
France

Phone : +33 (0)3 20 30 40 71
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