Something I should remember but can't! What do numbers to the power of Zero equal? To the power of one they are themselves and squared, cubed etc is obvious but zero?? Anyone remember
I don't see how that could ever be the style because $\displaystyle 0^0 $ isn't undefined because of tradition, it's because of the rules of powers.Originally Posted by ThePerfectHacker
$\displaystyle a^3 \cdot a^{-3} = a^{(3-3)} = a^0 = 1 $
or it could be written as...
$\displaystyle a^3 \cdot a^{-3} = \frac{a^3}{a^3} = 1 $
so $\displaystyle 0^1 \cdot 0^{-1} = 0^{(1-1)} = 0^0 = $undefined
or it could be written as...
so $\displaystyle 0^1 \cdot 0^{-1} = \frac{0^1}{0^1} = \frac{0}{0} = $ undefined
It appears to be still controversial, which means that unless anOriginally Posted by JakeD
author defines what they want it to mean, it is ambiguous and
hence undefined
This page has a good discussion and claims "Consensus has recently been built around setting the value of $\displaystyle 0^0 = 1.$"
I can't see why it could EVER be defined as one or the other since:Originally Posted by CaptainBlack
$\displaystyle \lim_{x \to 0}0^x \to 0$
and
$\displaystyle \lim_{y \to 0}y^0 \to 1$
As the limits do not agree we can't say that $\displaystyle 0^0$ is defined. What confuses me is why there is even discussion about defining it to be one or the other??
-Dan