Re: Relational operators on intervals: bug?

*To*: mathgroup at smc.vnet.net*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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <k7p3j3$ca3$1@smc.vnet.net> <20121112080708.39931690E@smc.vnet.net> <k7skt2$ku3$1@smc.vnet.net>

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.

**Follow-Ups**:**Re: Relational operators on intervals: bug?***From:*Andrzej Kozlowski <akozlowski@gmail.com>

**Re: Relational operators on intervals: bug?***From:*Murray Eisenberg <murray@math.umass.edu>

**References**:**Re: Relational operators on intervals: bug?***From:*Richard Fateman <fateman@cs.berkeley.edu>