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Re: Relational operators on intervals: bug?


On 11/12/2012 9:13 PM, Murray Eisenberg wrote:

>
> Here is the empty interval in Mathematica:
>
>    Interval[{1, 0}]
>
> Indeed:
>
>     Resolve[Exists[x, IntervalMemberQ[Interval[{1, 0}], x]]]
> False
>
Apparently this doesn't mean what you think it does. It gives the same 
answer for Interval[{0,1}].

Note that

IntervalMemberQ[ Interval[{1, 0}], 1/2]  is TRUE.

IntervalIntersection[Interval[{0, 1}], Interval[{1, 0}]]

is Interval[{0,1}].

That is, the endpoints, in Mathematica, are re-ordered. This is, in
my opinion, a bug.

Using your reasoning, there are an infinite number of ways of writing
an Interval with no "insides" -- why choose {1,0}?  A rather complete
calculus of interval including EXTERIOR intervals has been defined,
one in which {1,0} is the equivalent of the union of the (open)
intervals {-Infinity,0} and {1,Infinity}. A canonical representative
for an empty set would be useful in such a scheme.

The Mathematica implementation of Intervals seems to have a number
of design issues. I've commented on some of them, previously.



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