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.

A clear and intuitive answer can be provided by ZFC Set-Theory. As described in Enderton's 'Elements of Set Theory (available free for viewing here; see pdf-page 151): http://sistemas.fciencias.unam.mx/~lokylog/images/stories/Alexandria/Teoria%20de%20Conjuntos%20Basicos/Enderton%20H.B_Elements%20of%20Set%20Theory.pdf, the set of all functions from the empty set to the empty set consists merely of the empty function which is 1 function. Hence $0^0$ = 1.
