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Re: [IEEE P1788 er subgroup]: My first cut at the Level 1 list...

To: "R. Baker Kearfott" <rbk@xxxxxxxxxxxxx>
Cc: "stds-1788-er" <stds-1788-er@xxxxxxxxxxxxxxxxxxxxx>,
        stds-754@xxxxxxxxxxxxxxxxx,
        Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
From: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
Subject: Re: [IEEE P1788 er subgroup]: My first cut at the Level 1 list... Date: Wed, 25 Mar 2009 13:18:40 -0700


	Folks,

	We are currently having a discussion of the Level 1 issues
	in the ER subgroup.  One of the questions is pretty much
	the same as motion 3 so Baker asked if I would cross-post
	my opinion to the main reflector.

	I am having some technical difficulty with that but here
	goes.

	The links (1), (2), & (3) are references to some principles
	we are using to guide our discussion.  They are, in obvious
	homage to Asimov:


			The Three Laws of Interval Arithmetic

		(1) Return an interval encompassing the correct
		answer, if it exists, no exceptions.

		(2) Provide the means for the user to understand &
		manipulate at will exactly & clearly what is being
		done except in so far as such manipulation might
		invalidate a result.

		(3) Return the best possible answer except when
		doing so would conflict with the first two laws.

	With that context in mind, I include the comment below.

	Yours,

				Dan


Date: Wed, 25 Mar 2009 11:34:09 -0500
From: "R. Baker Kearfott" <rbk@xxxxxxxxxxxxx>
To: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
CC: stds-1788-er <stds-1788-er@xxxxxxxxxxxxxxxxxxxxx>
Subject: Re: [IEEE P1788 er subgroup]: My first cut at the Level 1 list...

Dan et al,

This particular question, whether or not the model should be R or
R*, is almost precisely the content of Motion 3, presently under
discussion on the main reflector.  For this reason, please also
consider posting your comments there.

Sincerely,

Baker

P.S. Contact me if you are still having trouble posting there.

On 3/24/2009 8:59 PM, Dan Zuras Intervals wrote:
> 	OK, folks,
>
.
.
.

>
> 	OK, from the top...
>
>
> 	Page 7, 3.1 Level 1 debates, 1a: Should the model be R or R*?
>
> 	I must admit that both the principles & I are largely agnostic
> 	on this point.  That having been said, I will argue in favor of
> 	R*.
>
> 	It seems to me that among the standard intervals the effective
> 	difference between R & R* boils down to the exclusion or
> 	inclusion of the two elements [-oo,-oo] & [+oo,+oo] in IR.
>
> 	While we can argue about the details of things like 1/[0,0],
> 	I think we can all agree that the function f(xx) = 1/(xx - 1)^2
> 	should be [+oo,+oo] when evaluated at xx = [1,1].
>
> 	It is true that (1) & (2) would permit us to return [+max,+oo]
> 	in this case but this would violate the best practices we want
> 	out of (3).
>
> 	So, I conclude we want R* but admit the case is weak.
>
>
.
.
.


--

---------------------------------------------------------------
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
---------------------------------------------------------------


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