Re: Empty interval representations & Motion 13...
On 2010-05-03 16:38:43 -0700, Dan Zuras Intervals wrote:
> > Subject: Re: Empty interval representations & Motion 13...
> > From: John Pryce <j.d.pryce@xxxxxxxxxxxx>
> > Date: Mon, 3 May 2010 17:20:24 +0100
> > To: P1788 <stds-1788@xxxxxxxxxxxxxxxxx>
> >
> > Dan & P1788
> >
> > I have gone through Dan's work on comparisons with the empty
> > set (below), checking against the set theory definitions given
> > in my mail earlier today.
> >
> > I think they all agree, except the two I have marked (*).
> > Namely I think
> > empty interior empty
> > empty strictLess empty
> > should both give True.
> >
> > Pretty good overall.
> >
> > John
>
> Well, nobody's perfect. :-)
>
> Still, I was using the endpoint comparison definition
> in that note & you recently raised the issue that we
> should, perhaps, consider a set theoretic definition.
>
> In that spirit, should we define:
>
> aa interior bb = there exists b1 & b2 in bb such
> that for all a in aa we have b1 < a < b2
Alternatively,
for all a in aa, there exist b1 and b2 in bb such that
b1 < a < b2
This definition is different for the empty interval and for the
unbounded ones. Which one is preferred?
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / Arénaire project (LIP, ENS-Lyon)