Re: Neumaier-Pryce proposed decoration system (v03.2)

["Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>]

Ok. Thanks for the clarification.

Yes, the decoration of sqrt(Empty) is "defined and continuous" in either
case, though it is also provably an element of the proper subset "defined
and continuous on empty input".

In my position, using the linear quality order to check the decoration is
greater-or-equal than D3 accomplishes what you are seeking:

Dominique Lohez wrote:
> IMHO the most significant comparison is between     decorated interval s
>
> sqrt([1,4]) = ([1,2], saf)
> sqrt(Empty)= (Empty,saf)
>
> and we have
> (Empty, saf) > ( [1,2], saf)
>
> We only need such a comparison

since for (Empty,D4) and ([1,2],D3)
   D4 > D3
is true.

I note that if the results were instead (Empty,D3) and ([1,2],D3), then
   D3 > D3
would be false, BTW.

Nate



----- Original Message ----- 
From: "Dominique Lohez" <dominique.lohez@xxxxxxx>
To: "Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>
Cc: "John Pryce" <j.d.pryce@xxxxxxxxxxxx>; "stds-1788"
<stds-1788@xxxxxxxxxxxxxxxxx>
Sent: Thursday, June 16, 2011 9:19 AM
Subject: Re: Neumaier-Pryce proposed decoration system (v03.2)


> Nate Hayes a écrit :
> > Dominique,
> >
> > I don't quite follow. Can you clarify?
> >
> > If we have the tracking results (by motion 25):
> >
> >    sqrt([1,4])
> >        = sqrt(([1,4],D3))    // promote input to "best" decoration
> >        = (sqrt([1,4]),inf(S(sqrt,[1,4]),D3))
> >        = ([1,2],inf(D3,D3))
> >        = ([1,2],D3)
> >
> >    sqrt(Empty)
> >        = sqrt((Empty,D4))   // promote input to "best" decoration
> The best decoration is now D3
> >        = (sqrt(Empty),inf(S(sqrt,Empty),D4))
> >        = (Empty,inf(D4,D4))
> >        = (Empty,D4)
> >
> > then we also have:
> The result is (Empty, D3)
> And the other conditions hold as well
> >    Empty \subset [1,4]    and    D4 \subset D3
> >
> > or, in motion 26 terms:
> >
> >    Empty \subset [1,4]    and    ein \subset dac
> >
> > so the tracking results are consistent with FTDIA.
> >
> > Or were you making some other point?
> >
> > Nate
> Dominique
>
> --
> Dr Dominique LOHEZ
> ISEN
> 41, Bd Vauban
> F59046 LILLE
> France
>
> Phone : +33 (0)3 20 30 40 71
> Email: Dominique.Lohez@xxxxxxx