# Questions tagged [tetration]

Tetration is iterated exponentiation, just as exponentiation is iterated multiplication. It is the fourth hyperoperation and often produces power towers that evaluate to very large numbers.

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### Possible real extension of tetration, or ones with similar growth rate; what makes it difficult?

This question arose when I read a (very introductory) googology book. Tetration is essentially repeated exponentiation (right-associative), just like how multiplication is repeated addition, defined ...
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### Golden Exponent? Tetration

I read somebody say “golden exponent $x^x=x+1$” now I didn’t understand what he meant but it really fascinated me thinking about some type of tetration version of the golden number. A number with a ...
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### Why does ${x}^{x^{x^{x^{\,.^{\,.^{\,.}}}}}}$ bifurcate below $\sim0.065$?

When you calculate what ${x}^{x^{x^{x\cdots }}}$ converges to between $0$ and $1$, before approximately $0.065$ the graph bifurcates. Why does this happen and is there a reason for it happens at that ...
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### Given a real number what is the minimum number of times it can be tetrated to get an intiger?

I really enjoyed this video on the possibility that $\pi^{\pi^{\pi^\pi}}$ is an integer, but i thought that it was a case of a more interesting general problem. Given a real $x$ and an integer $y$, ...
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### Estimates on growth of $^{n}3$

I was dealing with a problem on tetration and am supposed to explain why this problem was challenging to me- obviously, difficulties stemmed from the amazing growth of $^{n}3$. The question now is: Is ...