Re: Motion 13
On 2010-05-03 08:53:40 +0200, Ulrich Kulisch wrote:
> I think the problem with the empty set should be further discussed.
I agree.
> I have great sympathy with Dan's mail of April 22. I had very
> similar thoughts when I was working on my book. I studied modells
> representing the empty set by a tuple aiming to avoid the necessity
> of frequent checking for it. In a mail of April 22 Arnold Neumaier
> wrote:
> "This is just to let you know of Siegfried Rump's decision to remove
> empty intervals from Intlab Version 6;".
> This certainly is a very interesting remark. It is out of question
> that we need the empty set in interval arithmetic. But do we really
> have many applications where the empty set is used as an operand?
> In a mail of April 23 Juergen wrote:
> "I strongly propose to stay with our clear math. model and not to
> sacrifice the empty set for efficiency."
I think that the empty set should be regarded as some kind of
exception. But this isn't obvious. Some mathematical properties
(such as the subset inclusion yielding a lattice) would be true
only when the empty set is considered, while for others (ordering
between intervals yielding a lattice) it would be the opposite.
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Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / Arénaire project (LIP, ENS-Lyon)