> On the one hand, as said above, there is no way of defining 0^0 > using continuity, but on the other hand, many important properties > remain satisfied if we choose 0^0 = 1 (which is frequently > adopted, as a convention, by mathematicians). Kahan suggests to > choose 0^0 = 1. [...]
The problem is x^0.0 (real exponent), not x^0 (integer exponent). 0^0 (integer exponent) *can* be defined by continuity, the value is 1. The fact that it is defined by continuity is exactly the reason 0^0=1 is useful in contexts where the exponent is an integer (polynomials etc): the special case 0^0 acts the same as the general case x^0, since it is the limiting value of it. In my experience, defining 0^0.0 (real exponent) to be 1.0 is much less useful. Now in practice I can imagine that a language confuses x^integer and x^real by mapping them to the same function, or only provides a function for doing x^real. Perhaps this is the case with C? If so, then having 0^0.0 return 1.0 is a convenient hack to work around that mistake. On the other hand, ignoring such things as language standards and the weight of history, if there are separate functions for x^integer and x^real, then in my opinion the most sensible thing would be for 0^0 to return 1, and 0^0.0 to return NaN. This might confuse programmers though. All the best, Duncan.
