Zero to the Power of Zero/Derivatives
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Example of Zero to the Power of Zero
Consider the identity mapping:
- $\map {I_\GF} x = x$
where $\GF \in \set {\R, \C}$.
From Derivative of Identity Function:
- $\dfrac {\d I_\GF} {\d x} = 1$
But $\map {I_\GF} x = x^1$ is also an order one polynomial.
By Power Rule for Derivatives:
- $\dfrac {\d I_\GF} {\d x} = 1 x^0$
As $I_\GF$ is differentiable at $0$, for these theorems to be consistent, we insist that $0^0 = 1$.