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Topic: Relational operators on intervals: bug?
Replies: 21   Last Post: Nov 17, 2012 3:51 AM

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 Andrzej Kozlowski Posts: 226 Registered: 1/29/05
Re: Relational operators on intervals: bug?
Posted: Nov 16, 2012 2:14 AM

On 15 Nov 2012, at 09:57, Andrzej Kozlowski <akozlowski@gmail.com> wrote:

>
> On 14 Nov 2012, at 22:01, Murray Eisenberg <murray@math.umass.edu> wrote:
>

>> On Nov 14, 2012, at 5:39 AM, Andrzej Kozlowski <akozlowski@gmail.com> wrote:
>>

>>>
>>> On 14 Nov 2012, at 07:28, Richard Fateman <fateman@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

>>>
>>> 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
>
>

Maybe the following example will make my point clearer.

Compare:

Resolve[Exists[x, Element[x, Primes]]]

True

with

Resolve[Exists[x, PrimeQ[x]]]

False

Mathematica `predicates (functions ending with Q) always evaluate immediately to True or False and thus are generally unsuitable for use in symbolic expressions of the above kind.

Andrzej Kozlowski