On Sat, 12 Mar 2005 03:02:20 +0100, Gabriel Dos Reis <[EMAIL PROTECTED]> said: > David Carlton <[EMAIL PROTECTED]> writes: >> On Thu, 10 Mar 2005 15:54:03 +0100, Gabriel Dos Reis <[EMAIL PROTECTED]> >> said: >>> Vincent Lefevre <[EMAIL PROTECTED]> 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 [EMAIL PROTECTED]