Responding to Dan Zuras, Ulrich Kulisch wrote:
SHOULD the basis for our (interval) arithmetic be R or R*
(including -oo & +oo)?
The basis for real interval arithmetic is R*, of course,
the same as for floating-point arithmetic.
What does "basis for arithmetic" mean? Dan and Ulrich seem
to agree, but in fact they interpret this in the opposite way;
indeed, Dan's question was in response to Ulrich's pointing out
problems with including "Infinity as a Member" of an interval.
Dan's reason for preferring to include infinities was:
I thought that if we allow ourselves to use R* in designing
the underpinnings of intervals we should also allow our users
the same benefits.
So I chose R* but, as I said above, I admit that the case is
a weak one.
Earlier Dan had acknowledged the problem of dealing with poles of
odd order, as pointed out by Ulrich.
Meanwhile, Ulrich already voted (prematurely, I think -- the motion is
still in the discussion period) YES on motion M0003.01_Set_of_reals,
i.e. in favour of NOT allowing infinity as a member.
I am also in favour of motion M0003.01, and I agree that *arithmetic*
is carried out in R* (being IEEE 754 or at least 754-inspired), but the
semantics are different, which is also why some of the IEEE 754 rounding
rules involving infinity may have to be adjusted in an IA context (or
worked around on a case-by-case basis).
In the end, the term "R* as basis for arithmetic" can be as misleading as
the term "infinity as a number". Let's stick to "infinity as a member"!
Michel.
P.S. I'm not sure I like posting to both groups, as I'm sure every
member of the subgroup is also subscribed to the main group.
In my mail system this works out fine because one entry will
simply be a reference to the main entry. Ok, so I will in fact
only send to the main list, even though the CC: implies that it
should also go to the subgroup. I can do that since the mail
system is totally under my control!
Sent: 2009-03-30 20:56:38 UTC