Zero to the power of zero
It is determined by definition that 00 ≝ 1, as you cannot calculate it's value.
Explanation
We will investigate how you can decide to do this. To this end, we will solve
We treat the exponent between braces separately with l'Hôpital's rule and get
After substitution we write
This is one of the many explanations why 00 ≝ 1 is by definition so determined.
HistoryThe above calculation is actually not correct. L'Hôpital's rule was simply applied. Derivatives are used in that. The derivative of a function f (x) is only defined if the two limits of left and right to point x = a exist. The German mathematician August Möbius (1790 - 1868) described this calculation to justify the definition. |