I vote YES on: Motion P1788/M0032:midpoint -- voting period begins
> Date: Sun, 1 Apr 2012 15:11:20 -0500 (CDT)
> From: Ralph Baker Kearfott <rbk5287@xxxxxxxxxxxxx>
> To: stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
> Subject: Motion P1788/M0032:midpoint -- voting period begins
>
> P-1788:
>
> The voting period herewith
> begins. Voting will continue until after Tuesday, April 17, 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.
>
> Juergen: Please update the web page with this action.
>
> Acting secretary: Please record the transaction in the minutes.
>
> The motion appears in the private area of the IEEE P-1788 site:
>
> http://grouper.ieee.org/groups/1788/private/Motions/AllMotions.html
>
> As usual, please contact me if you need the password to the private
> area.
>
> Best regards,
>
> Baker (acting as chair, P-1788)
>
> P.S. Note that Motions 30, 31, and 32 are now all under vote.
> Please carefully consider each, and vote.
>
>
> --
> ---------------------------------------------------------------
> 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
> ---------------------------------------------------------------
Baker,
I asked that the text of the
motion be updated a few days ago.
And I vote YES on that motion.
Yours,
Dan
>
> To: Ralph Baker Kearfott <rbk@xxxxxxxxxxxxx>,
> "Corliss, George" <george.corliss@xxxxxxxxxxxxx>,
> wolff@xxxxxxxxxxxxxxxxxxxxxxxxxxx
> Cc: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
> From: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
> Subject: The text for motion 32 was amended...
> Date: Wed, 28 Mar 2012 07:28:05 -0700
>
>
>
> Baker, George, Juergen,
>
> I accepted a friendly amendment to motion 32 some time
> back. It was to the effect that the domain of the
> function at level 1 was the bounded non-empty sets.
>
> Please see to it that this is reflected in the posted
> text. You may use the text below.
>
> Thanks,
>
> Dan
>
> -----------------
>
>
> The midpoint function for bounded, non-Empty intervals
> ------------------------------------------------------
>
> At level 1: mid(X) = (inf(X) + sup(X))/2
>
> Properties: For intervals X & Y & when using midpoint to
> split an X into X1 & X2 we have
>
> X \subset (X1 \union X2)
> [inf(X),mid(X)] \subset X1
> [mid(X),sup(X)] \subset X2
> mid(X) \element-of (X1 \intersect X2)
> X \subset Y ==> if (inf(X)==inf(Y)) then mid(X)<= mid(Y)
> X \subset Y ==> if (sup(X)==sup(Y)) then mid(X)>= mid(Y)
>
> always. These are required. The first 4 properties are
> required for containment to hold. The last 2 for weak
> ordering.
>
> Coercion to level 2: For some implicit or explicit IFbar
> based on a some floating-point system F we have that
>
> mid_F(X) = if ((inf(X) == -\infty) && (sup(X) == +\infty)) then 0
> else if (round2Nearest_F(mid(X)) == +\infty)
> then nextDown_F(+\infty)
> else if (round2Nearest_F(mid(X)) == -\infty)
> then nextUp_F(-\infty)
> else round2Nearest_F(mid(X))
>
> Note that midpoint has been generalized to include Entire via
> the means of the arbitrary choice of zero as its midpoint.
> This choice is part of this motion. Midpoint is still not
> defined for Empty & any generalization to include Empty is
> not part of this motion.
>
> The coercion mid_F(X) always returns a finite result even
> when mid(X) is infinite in F.
>
> If, for any X & Y that live at level 2, we define intervals
> X1 & X2 to be the smallest representable intervals for which
> [inf_F(X),mid_F(X)] \subset X1 & [mid_F(X),sup_F(X)] \subset
> X2 we have
>
> X \subset (X1 \union X2)
> [inf_F(X),mid_F(X)] \subset X1 (trivially)
> [mid_F(X),sup_F(X)] \subset X2 (trivially)
> mid_F(X) \element-of (X1 \intersect X2)
> X \subset Y ==> if (inf_F(X)==inf_F(Y)) then mid_F(X)<= mid_F(Y)
> X \subset Y ==> if (sup_F(X)==sup_F(Y)) then mid_F(X)>= mid_F(Y)
>
> The first 4 assure containment. The last 2, weak ordering.