Re: Suggestion for 2.5
Hi Christian, you wrote:
> In the same vein, we could say that 0^0 is not determinate, since
> (exp(-a^2/x^2))^(x^2) is exp(-a^2) always, whatever a is, and its limit
> form is 0^0 as x goes to 0.
> Anyway, a powerful argument in favor of 0^0=1 could be that, if x goes
> to 0, x^x goes to 1. The principle of economy, which here translates as
> "use one variable to resolve the indeterminacy, then 2 if you can't",
> then backs up the case of 0^0=1.
I don't know such a "principle of economy", that makes a contradiction
simply disappear.
> True, 0^x is always 0 if x is nonzero. It means that x +-->0^x is not
> continuous at 0. Not really shocking IMO.
>
> CChris
AFAIK shocking or not shocking wasn't the question here.
Since I'm not a mathematician, all I can say is, that my teachers at
school, the authors of my math textbooks, and the people at
http://mathworld.wolfram.com/ say, that 0^0 is undefined.
>> From: Juergen Luethje <eu.lue at gmx.de>
<snip>
>> "0^0 is undefined. Defining 0^0 = 1 allows some formulas to be expressed
>> simply (Knuth 1997, p. 56), although the same could be said for the
>> alternate definition 0^0 = 0 (Wells 1986, p. 26)."
>> [http://mathworld.wolfram.com/Zero.html]
<snip>
Regards,
Juergen
--
Q: How many Microsoft engineers does Bill need to change a light bulb?
A: None. He just declares darkness to be an industry standard.
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