Re: P1788: Our first formal motion: IR versus *IR

[Ulrich Kulisch <Ulrich.Kulisch@xxxxxxxxxxx>]

The suggestion is:
1. to use the notation IR for the complete lattice of closed (bounded 
and unbounded) intervals over R with the empty set as the least element 
and the set  R = (-oo, +oo) as the greatest element.
2. to allow an index notation for intervals as an alternative.

As far as I understand an earlier mail by Arnold Neumaier;
the proposed StandardNotation uses the notation *IR for the set defined 
under 1. It restricts the symbol IR to the subset of non empty, closed 
and bounded intervals over R.

Ulrich Kulisch


R. Baker Kearfott schrieb:
> Ulrich et al,
>
> I don't see any contradictions between the proposed notation and
> what you say you would like.  What am I missing?
>
> Baker
>
> On 1/18/2009 6:37 AM, Ulrich Kulisch wrote:
> > John:
> >
> > I am very happy about your mail and I basically agree with it. But let
> > me make the following remark:
> >
> > IR certainly is the most natural notation for a set of real intervals
> > somebody is using. I feel a little sad if we (by voting) restrict this
> > simple notation to a set which is mathematically incomplete. With set
> > inclusion as an order relation IR is an ordered set and it is most
> > natural to take it as a complete lattice. The least element is the empty
> > set and the greatest element is the set (-oo, +oo). The infimum is the
> > intersection (which can be the empty set) and the supremum is the
> > interval (or convex) hull. (It is an inf-sublattice of the power set 
> > PR.)
> >
> > The past was a learning process for all of us. I am convinced that IR as
> > a complete lattice is the view intervals are considered by R. E. Moore.
> >
> > So whatever the StandardNotation for intervals will be I shall take the
> > freedom to denote the set of closed (bounded and unbounded) real
> > intervals by IR and I shall use an index notation for the bounds of
> > intervals whenever it is convenient.
> >
> > Best whishes
> > Ulrich Kulisch