What is 0 to the power of 0?
This is actually a matter of debate. Some mathematicians say
See the discussion on Wikipedia:
Exponentiation : Zero to the power of zero
Personally I like
Here's one argument in favour of
For any number
For any positive integer,
So what about
By analogy, that's an empty product - the product of
If we're happy with that, what about
If it's the empty product of
Unfortunately, if we look at fractional exponents, we get some nasty behaviour.
so you would hope
So exponentiation behaves badly in the neighbourhood of