Re: inconsistent refinement behavior

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• Subject: [mg131469] Re: inconsistent refinement behavior
• From: Alex Krasnov <akrasnov at cory.eecs.berkeley.edu>
• Date: Fri, 12 Jul 2013 02:49:57 -0400 (EDT)
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• References: <krj23l\$1jf\$1@smc.vnet.net> <20130711060248.8267169C4@smc.vnet.net>

```Firstly, x==0 also implicitly assumes that x is in Reals, since 0 is in
Reals, as the following examples demonstrate:

In:	Assuming[x==0, Refine[Element[x, Reals]]]
Out:	True

In:	Assuming[{Element[x, Reals], x==0}, Refine[Infinity/x]]
Out:	ComplexInfinity

Secondly, ComplexInfinity results from the unknown sign of x at 0, not any
property of complex numbers.

Alex

On Thu, 11 Jul 2013, Helen Read wrote:

> assumption x>0 or x>=0, you are implicitly assuming that x is an element
> of the Reals, so with either of these assumptions the result will be
> Infinity rather than ComplexInfinity.
>
> Recall that there is no ordering in the complex numbers.
>
> On 7/10/2013 3:22 AM, Alex Krasnov wrote:
>> The following behavior appears to be inconsistent:
>>
>> In:	Assuming[x==0, Refine[Infinity/x]]
>> Out:	ComplexInfinity
>>
>> In:	Assuming[x>0, Refine[Infinity/x]]
>> Out:	Infinity
>>
>> In:	Assuming[x>=0, Refine[Infinity/x]]
>> Out:	Infinity
>>
>> The third example should return unrefined given the first two examples. Is
>> there an explanation?
>>
>> Alex
>>
>
>
>
>

```

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