Re: On trits & tetrits...
> From: "Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>
> To: "Dan Zuras Intervals" <intervals08@xxxxxxxxxxxxxx>
> Cc: <stds-1788@xxxxxxxxxxxxxxxxx>
> Subject: Re: On trits & tetrits...
> Date: Fri, 9 Apr 2010 16:07:40 -0500
>
> Dan Zuras Intervals wrote:
> > Not quite, Nat.
> >
> > Its kind of the set theoretic equivalent of the
> > fundamental theorem of interval arithmetic.
> >
> > While it is true that assertions on the empty set are
> > vacuously true, we are not gathering assertions.
> >
> > We are mapping the function P(f,x) onto the elements
> > of the set {true, false} FOR ALL x in xx. Thus, the
> > definition:
> >
> > decorationP(f,xx) = { P(f,x) for all x in xx }
> >
> > must have the result {} (the empty set) if there are
> > no elements in xx because it must be true that:
> >
> > decorationP(f,xx) \contained decorationP(f,yy)
> > for all xx \contained yy.
> >
> > In particular, we must have that:
> >
> > decorationP(f,[empty]) \contained
> > decorationP(f,xx) \contained
> > decorationP(f,[entire])
> >
> > for all f & for all xx.
> >
> > Since the empty interval is trivially contained in all
> > intervals we must haved that decoration(f,[empty]) = {}
> > (the empty set).
> >
> > Don't you agree?
>
> As tempting as it may be to draw this conclusion, IMHO it is misleading.
> But I don't mean to be critical, since in regards to all the rest I think
> your idea is quite elegant and precise way to deal with decorations. I'd be
> happy to help do a new motion, if you're interested.
> Nate
Please, be critical.
That's why I posted it here: to find out if the idea had merit.
Its also why I didn't just make a motion: I only had the idea
an hour or so before I posted it so I could easily have missed
something obvious.
Is it my explanation that is misleading or something about the
concept itself?
I am an infamously poor writer so both are possible.
I must say I thought the stickyness problem would more concern
people than this.
This is just what is required for simple set containment.
So, please, detail your concerns for all to hear.
Perhaps there is a better writer out there who can do a better
job.
Dan