Zero to the zero power – is $0^0=1$? Could someone provide me with a good explanation of why $0^0=1$?
My train of thought:
$x>0$
$0^x=0^{x-0}=0^x/0^0$, so
$0^0=0^x/0^x=\,?$
Possible answers:

*

*$0^0\cdot0^x=1\cdot0^0$, so $0^0=1$

*$0^0=0^x/0^x=0/0$, which is undefined

PS. I've read the explanation on mathforum.org, but it isn't clear to me.

There are so many fantastic answers already, but no pictures which is sad. $0^0$ is undefined - is it the limited case of $x^0$, $0^x$ or $x^x$? The plots for $x^0$ (a line at 1) and $0^x$ (a line at zero) are boring, but $x^x$ is

Author/Site: Wolfram|Alpha
Publisher: Wolfram Alpha LLC
URL: https://www.wolframalpha.com/input/?i=plot+x%5Ex
Retrieval date: 6/2/2015
I don't always define $0^0$, but when I do, I define it as $1$.
