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Re: Relational operators on intervals: bug?


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




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