Re: P1788: Our first formal motion has entered its discussion period

["Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>]

> 2. Nate Hayes wrote;
>
> > The proper/improper property of Kaucher intervals coincides with the
> > existential/universal property of modal intervals and the +/- property 
> > of
> > directed intervals. So the following table summarizes standard
> > interpretations:
> >
> >    [a,b]          [b,a]        Description
> >    proper      improper    Kaucher intervals (Kaucher, Goldsztejn,
> et. al.)
> >    existential  universal   Modal intervals (M. Sainz, Gardenes, et. 
> > al.)
> >    +                -            Directed intervals (Popova, Markov, et.
> > al.)
>
> The discussion in Section 5 of
>    A. Neumaier,
>    Computer graphics, linear interpolation, and nonstandard intervals,
>    http://www.mat.univie.ac.at/~neum/papers.html#nonstandard
>    (contains the most recent version from January 3, 2009)
> shows that no deviation from the proposed notation standard is needed to
> discuss nonstandard intervals.

It is my point, i.e., it would be helpful to explicitly mention this in the 
document on standardized interval notation.


> It is unacceptable to enforce the modal notation (used in a minority
> of papers only), which adds unnecessary primes to the ordinary
> interval notation, upon the whole interval community.

I don't advocate such a thing. In my original e-mail I wrote:

"This notation generally is required only in discussions about modal
intervals."

Nate Hayes