RE: Undefined behaviour (Was: Definition of intervals as subsets...)
Dear Dan,
Just read the file I posted http://www.cs.utep.edu/vladik/modal.pdf , at least give it a start, modal intervals are not as straightforward as regular ones, this is one of the reasons why Arnold and many others want to avoid discussing them at this stage.
-----Original Message-----
From: stds-1788@xxxxxxxx [mailto:stds-1788@xxxxxxxx] On Behalf Of Dan Zuras Intervals
Sent: Monday, March 16, 2009 2:36 PM
To: Michel Hack
Cc: stds-1788; Dan Zuras Intervals
Subject: Re: Undefined behaviour (Was: Definition of intervals as subsets...)
> Date: Mon, 16 Mar 2009 15:59:57 -0400
> To: stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
> From: Michel Hack <hack@xxxxxxxxxxxxxx>
> Subject: RE: Undefined behaviour (Was: Definition of intervals as subsets...)
>
> Vladik Kreinovich wrote:
> > The explanation is simple: in Kaucher arithmetic, the interval ?5,2Ù
> > DOES NOT mean {x: 5<= x <=2}, this interpretation would lead to an
> > empty set.
>
> That's not how Dan interpreted it; he wrote:
> >> Can it really be that the sum of {x | 5 <= x or x <= 2} ...
>
> Note the OR, not AND. He interprets it as the union of two
> disjoint intervals [-oo,2] U [5,+oo].
>
> Michel.
> Sent: 2009-03-16 20:04:41 UTC
Michel is correct that that was my interpretation.
Let me put it yet another way: if I interpret [5,2]
exterior interval that is complement to the interior
interval [2,5], how can the sum of that exterior
interval which contains numbers like 10^10^10, when
added to the relatively tiny interior interval [3,9]
result in the EVEN TINIER interior interval [8,11]?
I'm sorry, if I am missing something obvious here it
still eludes me.
This case would, by my confusion alone, seem to
support the non-intuitive nature of these things.
Dan