Arnold Neumaier a écrit :
Dominique Lohez wrote:
Vladik, John, p1788
I completely agree with the fact that the set of interval
comparisons must be slim.
However it is not enough to state that to be conformant to the
Standard some interval comparison must be provided.
It must be stated in the standard that
NO ADDITIONAL COMPARISON MAY BE PROVIDED.
Otherwise you may be sure that some vendor will add some "very
convenient" comparison.
Yes, and what's wrong with that? Every programmer can add their own
comparison anyway.
I think I have misunderstood your position
What you require is that only three comparisons are mandatory in the
standard.
I think that the possibility for the user to introduce additional
comparison should be severely restricted.
The rationale is that adding new comparison may completely change the
mathematical nature of the intervals we are dealing with
To detail my position I consider the much more simple case of numbers.
If the only comparison allowed between numbers is Equality :
Then the comparable numbers may be integers, rational ,
floating point numbers, real numbers and even complex numbers .
If the less comparison is added The complex numbers are
no more comparable numbers
Furthermore comparable numbers can now be sorted,
intervals can be defined , etc
Thus we do not work with the same mathematical objects in both cases.
IMHO the standard should define the nature of the mathematical
objects we are working on.
In that context adding new comparisons should be discouraged, and
only left to users( and not vendors) who know what they are doing.