Motion 2 amendment and coming motions
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
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