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http://en.wikipedia.org/wiki/Tetration

Tetrating stuff makes it really big really fast. I'm trying to figure out what number would equal a googol. Any help?

Or a googolplex ?

dansch
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    Well, $3^{3^3}$ has $12$ digits and is much smaller than googol, where $4^{4^{4^4}}$ has $8.072\cdot 10^{153}$ digits, and is thus much bigger than googolplex. – Milo Brandt Mar 10 '15 at 23:32
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    @Meelo: I think that should be an answer; since real-valued tetration isn't particularly well-defined, it's hard to see how to do much better than that... – Micah Mar 10 '15 at 23:34
  • $$b_1 \approx 3.22192863; ; ;;; b_2 \approx 3.96367752$$ $$b_1 \uparrow \uparrow b_1 \approx 10^{100}$$ $$b_2 \uparrow \uparrow b_2 \approx 10^{10^{100}}$$

    Analytic extension of tetration results using http://math.eretrandre.org/tetrationforum/showthread.php?tid=486

     – Sheldon L Mar 12 '15 at 14:20

1 Answers1

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We use essentially guess and check.

Consider $X = 3$

Then:

$$Tetration(3,3) = 3^{(3^3)} = 3^{(27)}$$

Too small, lets try bigger

$$Tetration(4,4) = 4^{(4^{4^4})} = 4^{4^{256}} \text{~ ~} 4^{10^{155}} $$

That's getting better. Interpolating any further is tricky business and may require some specialized tools.

The users here: http://math.eretrandre.org/tetrationforum/index.php

Would probably be well equipped to answer your question

Sidharth Ghoshal
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