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

[David Carlton <david dot carlton at sun dot com>]

On Sat, 12 Mar 2005 03:02:20 +0100, Gabriel Dos Reis <gdr@integrable-solutions.net> said:
> David Carlton <david.carlton@sun.com> writes:
>> On Thu, 10 Mar 2005 15:54:03 +0100, Gabriel Dos Reis <gdr@integrable-solutions.net> said:
>>> Vincent Lefevre <vincent+gcc@vinc17.org> writes:
>>>> On 2005-03-10 01:01:18 +0100, Gabriel Dos Reis wrote:

>>>>> The asseryion that 0^0 is mathematically undefined is not a
>>>>> bogus reason. It is a fact.

>>>> I disagree. One can mathematically define 0^0 as 1. One often
>>>> does this.

>>> what you do is to set a local convention regardless of all
>>> mathematical absurdities you run into.

>> No, you follow the convention that all mathematicians that I know
>> of follow, because it's generally recognized as the most useful
>> one.

> Please given references -- not just unnamed mathematicians you claim
> to know.

I don't have my math books with me; sorry.  As far as "claim to know",
that's a little bit over the top; I suppose you could start at
<http://www.genealogy.ams.org/html/id.phtml?id=22517> and poke around,
if you're seriously worried that I don't in fact know any
mathematicians.

>> Maybe there are mathematical subcultures in which a different
>> convention (or no convention) is followed; I haven't spent time in
>> such cultures.  But if it's a "local convention", then it's one for
>> a very large value of "local".

> Please consider the limit of x^y when you have both x and y go to
> zero.

There isn't one, of course.  That doesn't prevent people from deciding
which convention is most useful.  After all, in general,
exponentiation isn't uniquely defined almost anywhere: for example, if
you fix y = 1/2, then you're looking at the square root function, and
numbers have two square roots.  So I can "prove" that 4^(1/2) isn't
well defined by taking the limit of x^(1/2) as x goes in a circle
around the origin in the complex plane, starting and ending at 4, and
getting the answer of 2 at the start and -2 at the end.  But people
pick a convention nonetheless, and say that 4^(1/2) = 2.

I'll admit that my background might be somewhat skewed, since I've
spent most of my time in areas that are relatively strongly influenced
by algebra, and there x^0 = 1 for all x is the only definition that
makes sense (because of polynomials, power series, etc.).  I would
think I'd spent enough time around analysts (for some values of
"analysts": complex analysts likely, real analysts probably, numerical
analysts very little) to know if they had another opinion on the
matter, but I'm less confident there: that's why I talked about other
mathematical subcultures.  Maybe the group that produced LIA-2 is such
a subculture.

David Carlton
david.carlton@sun.com