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.
