Jan Ingvoldstad wrote:
> On Thu, Oct 1, 2009 at 10:15 PM, Moritz Lenz <mor...@faui2k3.org> wrote:
>>
>>
>> What's the 0th root of a number, then?
>> It would be a number $y for which $y ** 0 == $x, which can only be
>> fulfilled for $x == 1. So in the general cases the answer to the
>> question root($x, 0) is nonsense, which is best mapped to NaN.
>>
>
> That doesn't make sense. The answer is 1, not NaN.
>
> Think about it for a while: mathematically speaking, we would expect the 0th
> root of a number to be 1.

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Excuse me?
given a number $x, roots($x, $n) returns a List (mathematically speaking
a Set) of numbers $y, for which $y**$n == $x holds true.
If roots(3, 0) returned 1, then 1**0 == 1, which is not 3. It's bettter
to return NaN to indicate an impossible operation, rather than to return
an ordinary number which is a wrong result.
It is not obvious to me why 1 or in fact any defined number at all would
be a mathematically sensible result - care to elaborate?
Cheers,
Moritz