Re: inconsistent refinement behavior

*To*: mathgroup at smc.vnet.net*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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*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: > There is nothing inconsistent about this. When you include the > 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 >> > > > >

**References**:**Re: inconsistent refinement behavior***From:*Helen Read <readhpr@gmail.com>