Re: Motion P1788/M0013.04 - Comparisons - Overflow / Infinity
> From: "Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>
> To: "Dan Zuras Intervals" <intervals08@xxxxxxxxxxxxxx>
> Cc: <stds-1788@xxxxxxxxxxxxxxxxx>,
> "Dan Zuras Intervals" <intervals08@xxxxxxxxxxxxxx>
> Subject: Re: Motion P1788/M0013.04 - Comparisons - Overflow / Infinity
> Date: Tue, 21 Sep 2010 09:20:38 -0500
>
> Dan Zuras wrote:
>
> . . .
>
> > And since we have only one such endpoint we can
> > have only one interpretation for an interval
> > possessing that endpoint. That is that we know
> > no bound for that interval.
> >
> >>
> >> Hence, [1,Infinity] is a closed, unbounded interval, but [1,Overflow] is
> >> a
> >> compact interval with a "really big" (but finite) upper bound.
> >
> > Well, first, I think of [1,infinity] as a semi-open
> > interval.
>
> Technically, [1,Infinity] is a closed, unbounded interval:
>
> http://mathworld.wolfram.com/ClosedInterval.html
I read it.
Its not right.
Technically one does not close an infinity.
Not topologically anyway.
Not from an open set that does not contain
infinity as an element.
We have a representation of infinity but it
is not a member of the Reals.
We extend the Reals in the sense that we know
how to say when a subset of the Reals has no
bound.
But none of this matters.
Its just words.
Call it bounded if you like.
Call it Nancy if you like.
The only thing that matters is we have only
one infinite endpoint.
How we think about it is just rationale.
Sometimes it helps us sleep at night.
Sometimes we lay awake.
>
> > And, second, whether we know no bound because there
> > is no bound or we know no bound because we were unable
> > to compute & represent that bound amounts to the
> > same thing: we know no bound.
> >
> > For us these are the same.
>
> Then you just made an argument there should be no IsBounded decoration.
Not the way it is, no.
I argued for a slightly different decoration in
the past for slightly different reasons.
The decoration I feel we should be using for this
could be called aBoundIsKnown. The thing that
would be saved (made sticky) is when its false
which could be called NoBoundIsKnown.
And it happens when the 754 overflow flag happens.
Simple.
>
> . . .
>
> >
> > John is also right historically: it has always
> > been hard to deal with the infinite.
>
> I fully agree! :-)
>
> THis is why I'm glad we have people like John and Arnold to make sure we
> stay within proper mathematical boundaries, however controversial some of
> the proposed suggestions or ideas might otherwise be.
>
> Sincerely,
>
> Nate
I agree as well. Those of us on the 754 committee
would often make mistakes about infinity. I made
as many as the next guy. We had each other to
keep us honest. We have that here as well.
The only distinction is that in 754 we had a common
conceptual framework for thinking about infinity.
Even then, arguments would still happen.
Infinity is hard.
Dan