Re: Relational operators on intervals: bug?

*To*: mathgroup at smc.vnet.net*Subject*: [mg128665] Re: Relational operators on intervals: bug?*From*: Andrzej Kozlowski <akozlowski at gmail.com>*Date*: Thu, 15 Nov 2012 03:57:35 -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> <20121114062826.C02FC69AC@smc.vnet.net> <6F6D7B27-201F-4AC9-9553-809ABA30A7CE@mimuw.edu.pl> <9488D537-DAE3-45F6-A088-38486CB999AB@math.umass.edu>

On 14 Nov 2012, at 22:01, Murray Eisenberg <murray at math.umass.edu> wrote: > On Nov 14, 2012, at 5:39 AM, Andrzej Kozlowski <akozlowski at gmail.com> wrote: > >> >> On 14 Nov 2012, at 07:28, Richard Fateman <fateman at cs.berkeley.edu> wrote: >> >>> 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}]. >> >> Of course that is because >> >> IntervalMemberQ[Interval[{0, 1}], x] >> >> False > > What remains surprising to me is: > > Resolve[Exists[x, x \[Element] Reals, IntervalMemberQ[Interval[{0, 1}], x]]] > False > I don't find it surprising. All you are doing is, evaluating Exists[x,Element[x,Reals],False] which is False and then Resolve[False] which is also False.The fact that IntervalMemberQ[Interval[{0, 1}], x] immediately evaluates to False (unlike, for example, 0<x<1, which evaluates to itself) is responsible for this and shows that IntervalMemberQ is not intended to be used in symbolic expressions. Compare this with Resolve[Exists[x, x \[Element] Reals, 0 < x < 1]] True Andrzej Kozlowski

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

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

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