Tagged Questions

If iterated exponentiation (usually also called "Powertower") is understood as mathematical operator or as function depending on the iteration height, then this operator/operation/function is often called "tetration" and is assumed as next step in the operator hierarchy addition,multiplication, ...

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Tetration graph for this function

I'm trying to visualize the derivatives of exponential tetration, by taking the original equation from its graph. Right now there is no elementary way of expressing the derivative. I'm not allowed to ...
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A question on the equation $^qx=2$

Given the equation $$^qx=2$$ with $q\gt3$ where $^qx$ means the 'tetration' operation on $x$, my question is: is it possible to find a value for $q$ for which the solution $x$ of the equation is a ...
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Efficient algorithm for calculating the tetration of two numbers mod n?

I'm trying to study the algebraic properties of the magma created by defining the binary operation $x*y$ to be: $x*y = (x \uparrow y) \bmod n$ where $\uparrow$ is the symbol for tetration. ...
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Is the exact value of $^{\infty}i$ known? [duplicate]

Wikipedia's article on tetration has a table of successive tetrations of $i$ that seems to imply that $^{\infty}i$ converges, and my own experimentation seems to confirm it, but I'm suspicious of ...
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Tetration of Alephs

Does this even mean anything? $\underbrace{x^{x^{x^{...^{x^x}}}}}_n$ Where $n = \aleph_0$? Because I "know" it converges when (say) $x = .5$ and $n \to \infty$
For each $n$, define $f_n:\mathbb R^+\rightarrow \mathbb R^+$ by $f_n(x) = \underbrace{x^{x^{x^{...^{x^x}}}}}_n$ Is it true that $\lim\limits_{n \to \infty} f_n(\frac{n+1}{n}) = 1$ ? A few ...