Re: I vote NO on: Motion P1788/M0032:midpoint
On 2012-04-02 14:04:22 +0200, Vincent Lefevre wrote:
> * "to be the smallest representable intervals"
>
> It seems that Dan Zuras uses "smallest" to mean here a minimal element
> for the partial order. I don't think the wording is correct, making
> the motion ambiguous. See the different notions here:
>
> http://en.wikipedia.org/wiki/Partially_ordered_set#Extrema
>
> Note that "smallest" or any minimality notion is useless here
> (if the properties are true for X1 and X2, they remain true for
> any supersets of X1 and X2). So,
>
> "to be the smallest representable intervals"
>
> could be replaced by "to be any representable intervals".
In fact the whole part
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)
doesn't depend on the definition of the midpoint: this remains true
for any mid_F function such that:
inf_F(X) <= mid_F(X) <= sup_F(X)
(and if this property were not true, writing [inf_F(X),mid_F(X)] and
[mid_F(X),sup_F(X)] would be meaningless). So, I think that it would
be better to remove this part from the motion, and perhaps replace it
by the more important property: inf_F(X) <= mid_F(X) <= sup_F(X), as
I've already mentioned in my 2012-03-15 mail.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)