Re: Disjoint, subset, & interior, or more...???
On 10/3/2010 17:54, Dan Zuras Intervals wrote:
Folks,
I have been having an offline discussion with John about
these comparison issues. He has (indirectly) convinced
me that I should make my concerns more public.
.
.
.
You see, my attraction to his limited set of comparisons
is partially pedegogical rather than technical. Sooner or
later we are going to have to deal with users of interval
software who are trained to think in floating-point rather
than interval terms. The natural tendency will be to
attempt to convert their floating-point algorithms to
interval ones by, more or less, declaring all their
floating-point variables to be intervals instead.
On the other hand, although 754 may not be perfect in this
regard, it DOES provide an excellent framework upon which basic
interval operations can be built. In particular, I am thinking
of the directed roundings, as well as recommended elementary functions
(along with accuracy requirements). It would be a shame (in my own opinion) not
to take full advantage of what we can in crafting 1788. The +/-0 and
behavior of \infty may have been designed with interval continued
fractions in mind, and that might be at odds with the most
desired behavior in other applications.
This would be, of course, a HUGE mistake.
And what better way to convince them that it is a mistake
than to hit them right away with the fact that you cannot
compare two intervals as you once compared two floating-
point values? Sure, some of them would try to hack around
it. But at least some of them would look into why this is
the case&, just perhaps, learn something about how to do
REAL interval calculations. Correct interval calculations.
I personally find Juergen's Motion 21 attractive in this regard.
It provides all possible comparisons, viewed in terms of the
ordering on the reals, yet encompassing what we would desire
with respect to set inclusion. (Granted, some things we want
would be compound operations, but we get both the numerical ordering
and the set inclusion ordering with this set.)
Its worth a shot, if for no other reason than that.
But back to the technical issue, I am not convinced by
Arnold's big 3: disjoint, subset,& interior. I'm OK with
the first two but the 3rd bothers me.
.
.
.
I believe Baker is correct that someone should make some
sort of unifying or simplifying motion on this matter.
And I feel eminently unqualified to do so.
A couple of other people have expressed similar sentiments. I am willing
to actually make that motion, just to move things along, if Arnold is still
unwilling to formally register and participate officially. However, it may
add to the confusion if such a motion is put forward before 13.04, 20, and 21 are
processed. What do you think?
I am asking for your help.
Just say the word.
Best regards,
Baker
Dan
--
---------------------------------------------------------------
R. Baker Kearfott, rbk@xxxxxxxxxxxxx (337) 482-5346 (fax)
(337) 482-5270 (work) (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
---------------------------------------------------------------