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Re: Motion 31 draft text V04.4, extra notes

On 2012-04-17 08:42:02 -0500, Nate Hayes wrote:
> Vincent Lefevre wrote:
> >Since there is no practical difference, between Inf and OVR, I don't
> >see why you are complaining about unbounded intervals.
> I may ask the same question of you about OVR.

No, because:
  * OVR isn't defined at Level 1 (as you said). This would mean
    that Level 2 functions would get arbitrary choices that you
    need to justify in the standard (currently the Level 2 results
    directly come from Level 1 properties: if a Level 1 result is
    X, then a Level 2 result is an interval containing X).
  * Manipulating intervals is much easier than manipulating families
    of intervals.

> But instead, let me point out you have agreed (several times) unbounded
> intervals are unnecessary.

No, I haven't... unless you come with a model that is more powerful
(at Level 1 and Level 2) than the current one, with all the details
and the proofs. If it is just equivalent and more complex to explain,
I'm not interested.

> >Level 1 will never occur in the implementation of the standard. On your
> >side, you can use whatever you like for math equations.
> This applies to you, as well.

??? You haven't understood. Level 1 is there to specify Level 2.
If things like OVR are specified at Level 2 only, there's something
missing.

-- 
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)