On Mon, 2005-03-07 at 10:51 -0500, Robert Dewar wrote: > Paolo Carlini wrote: > > Andrew Haley wrote: > > > >> F9.4.4 requires pow (x, 0) to return 1 for any x, even NaN. > >> > >> > > Indeed. My point, basically, is that consistency appear to require the > > very same behavior for *complex* zero^zero. > > I am not sure, it looks like the standard is deliberately vague here, > and is not requiring this result.
Mathematically speaking zero^zero is undefined, so it should be NaN. This already clear for real numbers: consider x^0 where x decreases to zero. This is always 1, so you could deduce that 0^0 should be 1. However, consider 0^x where x decreases to zero. This is always 0, so you could deduce that 0^0 should be 0. In fact the limit of x^y where x and y decrease to 0 does not exist, even if you exclude the degenerate cases where x=0 or y=0. This is why there is no reasonable mathematical value for 0^0. Ciao, Duncan.
