Re: Relational operators on intervals: bug?
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- Subject: [mg128653] Re: Relational operators on intervals: bug?
- From: Richard Fateman <fateman at cs.berkeley.edu>
- Date: Wed, 14 Nov 2012 01:28:26 -0500 (EST)
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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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- From: Andrzej Kozlowski <akozlowski@gmail.com>
- Re: Relational operators on intervals: bug?
- From: Murray Eisenberg <murray@math.umass.edu>
- Re: Relational operators on intervals: bug?
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- Re: Relational operators on intervals: bug?
- From: Richard Fateman <fateman@cs.berkeley.edu>
- Re: Relational operators on intervals: bug?