RE: Oops, restatement Re: Motion P1788/M0037.01:MidAndRadSpecs: provisional NO
I would suggest mid(Empty) = NaN, since we want mid to be an element of the original interval.
If we define radius as the smallest non-negative real F-number for which [mid - rad, mid + rad] contains the original interval, then, since an empty set is contained in everything, we naturally get rad(Empty) = 0.
-----Original Message-----
From: Ralph Baker Kearfott [mailto:rbk@xxxxxxxxxxxx]
Sent: Sunday, October 21, 2012 6:25 AM
To: John Pryce
Cc: stds-1788; Kreinovich, Vladik; Ralph Baker Kearfott
Subject: Oops, restatement Re: Motion P1788/M0037.01:MidAndRadSpecs: provisional NO
Oops, "here I go again." I meant:
Does anyone have a strong opinion on whether Wid(Empty) = NaN or Wid(Empty) = -\infty? or something else?
^ ^
Baker
====================
Does anyone have a strong opinion on whether mid(Empty) = NaN or mid(Empty) = -\infty? or something else?
Baker
On 10/21/2012 03:30 AM, John Pryce wrote:
> P1788
>
> I vote NO, on the grounds that mid and rad of Empty were omitted from the motion, see my recent queries appended. I will change my vote to YES as soon as this is satisfactorily clarified.
>
> Chair: This doesn't change what the motion currently specifies, but only adds to it, so I hope we can just carry on voting after this clarification.
>
> IMHO the only sensible value for mid(Empty) is NaN. Any real value falsifies the Level 2 invariant mid(xx) \in xx, which holds in all other cases. For rad(Empty), I'm easy between -oo and NaN with a small preference for -oo, on the grounds that I also slightly prefer wid(Empty) to be -oo.
>
> John Pryce
>
> On 20 Oct 2012, at 23:30, Ralph Baker Kearfott wrote:
>> The voting period herewith
>> begins. Voting will continue until after Saturday, November 10, 2012.
>> Voting on this motion will proceed according to the rules for
>> position papers (quorum and simple majority).
>> Comment can continue during voting, but the motion cannot be changed
>> during voting.
>
> On 19 Oct 2012, at 15:48, John Pryce wrote:
>> What do you want midpoint(Empty) to be? Not also 0 by natural symmetry, I hope?
>
> On 19 Oct 2012, at 18:06, John Pryce wrote:
>> ... IMO the correct recipe is
>> wid(xx) returns the smallest F-number ≥ the mathematical width xhi-xlo.
>>
>> Vladik: what is the Level 2 width of Empty? I would be happy with
>>
>> NaN, on the grounds that it is genuinely undefined; or
>> -oo, on the grounds that wid(xx) = (sup xx) - (inf xx), and when
>> xx=Empty, one has sup xx = -oo and inf xx = +oo.
>
>
--
---------------------------------------------------------------
Ralph 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
---------------------------------------------------------------