# Some tetration you got there

Calculus Level 4

$\LARGE f(x;n) = \underbrace{ x^{x^{.^{.^x}}} }_{\text{number of } x \text{'s } =\ n }$


A positive integer $$n$$ is randomly chosen between 1 and 10000 inclusive for the function described above.

If $$p$$ denotes the probability that $$\displaystyle \lim_{x \to 0} f(x;n) = 1,$$ what is the value of $$\left \lfloor 1000p \right \rfloor$$?

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