Editing Tetration (section)

==== Base zero ====
The exponential <math>0^0</math> is not consistently defined. Thus, the tetrations <math>\,{^{n}0}</math> are not clearly defined by the formula given earlier. However, <math>\lim_{x\rightarrow0} {}^{n}x</math> is well defined, and exists:<ref>{{cite web |url=https://math.blogoverflow.com/2015/01/05/climbing-the-ladder-of-hyper-operators-tetration/ |title=Climbing the ladder of hyper operators: tetration |series=Stack Exchange Mathematics Blog |website=math.blogoverflow.com |access-date=2019-07-25}}</ref>
:<math>\lim_{x\rightarrow0} {}^{n}x = \begin{cases}
  1, & n \text{ even} \\
  0, & n \text{ odd}
\end{cases}</math>

Thus we could consistently define <math>{}^{n}0 = \lim_{x\rightarrow 0} {}^{n}x</math>. This is analogous to defining <math>0^0 = 1</math>.

Under this extension, <math>{}^{0}0 = 1</math>, so the rule <math>{^{0}a} = 1</math> from the original definition still holds.