I strongly feel that we should deliberately avoid this term, because
I have seen two contradictory interpretations already -- both derived
from the words themselves:
(a) Intervals contain numbers, so it means that intervals can contain
Infinity as a member.
(b) Infinity stands for an arbitrarily large real number, as opposed
to IEEE 754 Infinity, which is NOT a real number, and is never a
member of an interval (but is used as a bound to denote the absence
of a real-number bound).
Part of the confusion may come from IEEE 754, where Infinity is deemed
to be *numeric*, but not a finite number.
I suggest we use the term "Infinity as a MEMBER" to distinguish the two
ways that infinities can participate in Interval Arithmetic.
(In terms of the Vienna proposal, the question is whether isIn(Inf, xx)
can be true or not. Well, as the Vienna Proposal now stands, it is always
false, because (for definiteness, at least, and presumably also because
of the author's preference) the proposal does take a stand on the issue.
The framework of the proposal is however a good starting point for both
points of view.)
Michel.
Sent: 2009-03-02 03:57:16 UTC