Re: Empty interval representations & Motion 13...
> Subject: Re: Empty interval representations & Motion 13...
> From: John Pryce <j.d.pryce@xxxxxxxxxxxx>
> Date: Tue, 4 May 2010 08:38:58 +0100
> To: P1788 <stds-1788@xxxxxxxxxxxxxxxxx>
>
> . . .
>
> 3.
> The definition of "aa interior bb" is also open to debate.
> Do we take the general topological definition, which is
> (all a in aa)(exist neighbourhood N of a) N \subseteq bb ?
> If so, then empty is interior to anything because of the initial "all".
>
> That is what I would prefer, and at least for empty it agrees with
> Nate's C++ guide.
>
> However, this also implies that if aa=[a1,a2] and bb=[b1,b2] are
> nonempty, then "aa interior bb" is equivalent to
> (b1 == -oo or b1 < a1) and (b2 == +oo or a2 < b2),
> in other words, the < conditions are only required at
> _finite_ endpoints of bb. E.g.,
> [2,+oo] interior [1,+oo] gives true.
>
> Do people agree with that?
I kinda do. What say you to:
aa interior bb = (b1 = -oo or (there exists b1 in bb such
that for all a in aa we have b1 < a)) and (b2 = +oo or
(there exists b2 in bb such that for all a in aa, a < b2))?
Let's see, that means
empty interior anyNonEmpty
anything interior entire
entire interior entire
but not
empty interior empty
anyNonEmpty interior empty
>
> > So -4 for Nate, +1 for John, +1 for Dan, I think.
OOoo, do I get another point?
> Hopefully, (+ a few) for P1788's working methods.
>
> John
Baker, let 1788 take several points out of petty cash.
And take a few for yourself.
You deserve them for putting up with the rest of us.
I have some small experience in this matter.
(Do I ever... :-)
I like working this way.
Beats the hell out of being chairman.
Sorry Baker :-).
But better you than me.
Dan