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A book claims that $9(9_9) = 9^{387420489}$.

I've never seen such an expression, and I've been unable to find anything about it on Google...

How is it supposed to be evaulated?

For reference, the name of the book is Pasatiempos curiosos e instructivos and this is the page where the expression appears (it's in Spanish but I can provide a translation if needed):

Book photo

kikones34
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  • Sin la definición formal de $;9(9_9);$ es imposible entender nada --- Without the formal definition of $;9(9_9);$ it is impossible to understand what's going on. – DonAntonio Oct 08 '16 at 09:47
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    $9^9=387420489$, so I guess $9(9_9)$ here just means $9^{9^9}$. I've never encountered that notation, though. Is it the only place where the book uses it? But maybe the original manuscript contained $9^{(9^9)}$ and person who was typesetting it had no idea what it meant and typeset it incorrectly. – celtschk Oct 08 '16 at 09:51
  • Check this newer notation for the same. Then we can write $$9\uparrow\uparrow 3=9(9_9)=9^{9^9}$$ – Masacroso Oct 08 '16 at 10:21

2 Answers2

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Since $9^9=387,420,489$, I assume that it’s a way of writing $9^{9^9}$. I don’t read Spanish, but that appears to be a discussion of attempts by Arab mathematicians to write large numbers using only three digits; if that’s the case, we’re looking at a historical special-purpose notation that didn’t survive.

Brian M. Scott
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  • That's the case, and seeing how nobody's seen this notation before, I think it's pretty safe to assume that it's indeed a historical notation that didn't survive. I think it probably was meant to be $9_{(9_9)}$ though, otherwise it doesn't make any sense. – kikones34 Oct 08 '16 at 13:04
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$9_9$ seems to be a strange notation of $9^9$, since $9^9 = 387,420,489$.

adjan
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