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 >