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Re: Do I have a second? Re: a draft motion on midpoint and radius

Ok. With #2 as my only outstanding comment for the discussion period, I second the motion.
 
Nate
 
 
Sent: Friday, September 28, 2012 9:09 AM
Subject: RE: Do I have a second? Re: a draft motion on midpoint and radius
 
I am ready to submit it as a proposal, sorry for the confusion
 
P.S. I am logging off, we fly back early morning tomorrow, I will be without reliable connection for a day or two when traveling
 
From: Nate Hayes [nh@xxxxxxxxxxxxxxxxx]
Sent: Friday, September 28, 2012 8:06 AM
To: rbk@xxxxxxxxxxxxx; Kreinovich, Vladik
Cc: stds-1788@xxxxxxxx
Subject: Re: Do I have a second? Re: a draft motion on midpoint and radius

Dear Baker,
 
Two comments:
 
1. I like these Level 2 definitions and would second, but I also notice the motion was submitted as a draft... is Vladik and/or Sigfried ready to submit the motion?
 
2. These appear to be Level 2 definitions, and I notice they contradict the Level 1 definitions in the current draft text (or at least the last version I had a chance to read carefully). It may be worth noting this and perhaps leaving that question to a future motion if it will not be addressed right now?
 
Nate
 
 
Sent: Friday, September 28, 2012 8:35 AM
Subject: Do I have a second? Re: a draft motion on midpoint and radius
 
P-1788:

Do I have a second to this motion?

Baker

On 09/28/2012 08:17 AM, Kreinovich, Vladik wrote:
> This motion about midpoint and radius is based on the
> discussions during our 2012 annual meeting at SCAN'2012,
> specifically on the idea proposed by Siegfried Rump:
> *******************************************************
> Definition of the _midpoint_ of an interval [a,b]:
>
> * we compute the mathematical midpoint
> (a + b) / 2 in the extended real line (whenever it is
> possible), and then take a finite computer representable
> floating point number which is the closest to this mathematical
> midpoint; if there are two closest numbers, we use rounding to
> even, i.e., select the one whose binary expansion ends in 0
>
> * the only interval for which the mathematical midpoint is not
> defined is the interval (-oo, +oo); for this interval, natural
> symmetry prompts us to define the midpoint as 0;
>
> Examples:
>
> * for an interval [a, +oo) with finite a, the midpoint is the
> number closest to +oo, i.e., MAXREAL
>
> * for an interval (-oo, a) with finite a, the midpoint is the
> number closest to -oo, i.e., -MAXREAL
>
> * for an interval [1, 1 + u], where 1 + u is the number closest
> to 1, the mathematical midpoint is 1 + (u / 2), so the closest
> numbers are 1 and 1 + u; rounding to even results in 1 being
> the desired midpoint
>
> Please note that a midpoint is, in general, different from a
> bisection point used to bisect an interval in different
> interval algorithms
> ************************************************************
> For any interval [a, b], once its midpoint m is defined, we can
> define its _radius_ r as the smallest computer representable
> floating point number (finite or infinite) for which the
> interval [m - r, m + r] contains the original interval [a, b].
>
> Examples:
>
> * for the interval [1, 1 + u], the radius is u
>
> * for the intervals [a, + oo) and (-oo, a), the radius is oo;
> this example shows the need for using an infinite number.
>


--

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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
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