Re: __builtin_cpow((0,0),(0,0))

[Marcin Dalecki <martin at dalecki dot de>]

On 2005-03-07, at 17:09, Duncan Sands wrote:
> Mathematically speaking zero^zero is undefined, so it should be NaN.

I don't see the implication here. Thus this certain is no 
"mathematical" speak.

> 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.

There is no deduction involved here. If you want to speak 
"mathematically" please
use the following terms: functions definition domain, continuous 
function
and so on... You wouldn't then sound any longer like a pre-Newtonian
mathematician needing a lot of words to describe simple concepts like
smoothness or derivability at least.

>  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.

There is no reason here and you presented no reasoning. But still there 
is a
*convenient* extension of the definition domain for the power of 
function for the
zero exponent.