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Dear Frédéric & P1788 On 8 Sep 2009, at 06:36, Frédéric Goualard wrote:
I am still confused here. I understand your point regarding the variouslevels (also raised by Prof. Neumaier in one of his recent mails). However, if, say, [-oo, -oo] is considered an invalid *notation* that shall not be identified with the empty set, what are our options tohaving it handled when time comes? I believe it can either be identifiedwith some "exceptional" interval (viz. NaI), or the program has to "break" (flag raising, exception raising, or whatever is available in the programming language considered). Both ways do not make me happy. Hence my NO vote on this motion; I cannot foresee a satisfying way of defining the levels that are not the subject of this motion given whatwould be defined in the levels it considers. I would be more than happyto be proved wrong, in which case I would gladly reverse my vote.
Ah yes. I share your concerns. But I don't see that voting no on motion 6 avoids the difficulties.
- There are bound to be interval constructors, for instance in a C++
"double" version, we surely can't avoid one that looks like
interval(double x, double y)
- Then you can't avoid the fact that possible calls are
interval(Inf, Inf)
interval(NaN,3)
interval(4,3)
The system has to respond to these invalid calls in SOME way.
Frédéric: what would YOU have it do?
I think George Corliss has made some some crucial points in his email "Tagged intervals (Was Branch & bound for not everywhere defined constraints)" of 5 September. These are relevant to this discussion and have made me modify my views on returning NaI, raising flags, etc. I will respond to that in more detail as soon as I can.
Regards John Pryce