How to define the $0^0$? Possible Duplicate:
  Zero to zero power  




According to Wolfram Alpha:


  $0^0$ is indeterminate.


According to google:
$0^0=1$

According to my calculator: $0^0$ is undefined

Is there consensus regarding $0^0$? And what makes $0^0$ so problematic?
This question will probably be closed as a duplicate, but here is the way I used to explain it to my students:

Since $x^0=1$ for all non-zero $x$, we would like to define $0^0$ to be 1. but ...

since $0^x = 0$ for all positive $x$, we would like to define $0^0$ to be 0.

The end result is that we can't have all the "rules" of indices playing nicely with each other if we decide to chose one of the above options, it might be better if we decided that $0^0$ should just be left as "undefined".
Define $f(x)=x^x$ and compute $\lim_{x\to 0} f(x)$.