Subject: Is Dr. Math wrong? (Re: [Maxima] 0^0 question)
From: Jay Belanger
Date: Fri, 25 Apr 2003 11:40:06 -0500
"Barton Willis" <willisb@unk.edu> writes:
> 0^0 is a can of worms; Stavros and I chatted about it awhile ago
> with no resolution. To understand some of the issues, you might
> like to start with
>
> http://mathforum.org/dr.math/faq/faq.0.to.0.power.html
>
> I proposed a new Maxima function, call it pow, such that pow(x,0)
> evaluates to 1 for all real or complex numbers x. Such a function
> would be useful inside summations, where we generally _do_ want 0^0
> to evaluate to 1.
But where _don't_ we want 0^0 to evaluate ot 1?
Not wanting to open a can of worms, but not sure how to avoid it, why
do we want to avoid setting 0^0=1?
I can think of several reasons why 0^0 should be 1, and none really
that it shouldn't. I've seen several mentions along the lines of
For certain f(x), lim_{x -> 0} f(x) doesn't exist, so
f(0) shouldn't exist
which I don't really buy.
The Dr. Math article mentioned discusses it, and ends with
Consensus has recently been built around setting the
value of 0^0 = 1 .
That's how I've always understood it, also. Is Dr. Math wrong?
Jay