Barton Willis <willisb at unk.edu> writes:
...
>>"Some textbooks leave the quantity 0^0 undefined, because the
>> functions x^0 and 0^x have different limiting values when x
>> decreases to 0. But this is a mistake. We must define x^0=1 for all
> x,
>> if the binomial theorem is to be valid when x=0, y=0, and/or x=-y.
>> The theorem is too important to be arbitrarily restricted! By
>> contrast, the function 0^x is quite unimportant."
>>
>
> Mostly off topic: I like "Concrete Mathematics" a great deal, but this
> reasoning is just plain hokie. All this would be better expressed
> by something like: If we don't agree that 0^0 = 1, we would need to peel
> the
> first term off from most the summations in this text.
Well, the binomial theorem is important for much more than that one
text.
> That would be ugly. Instead, let's agree that 0^0 = 1. In other
> contexts, the definition 0^0 = 1 might not be a good thing.
When would it be a bad thing?
Jay