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How do I browse very large numbers in mathematica, say $10^{{10}^{{10}^{1.414\ldots}}}$?

By browse I mean finding the $k$th decimal place before or after the decimal point. Everything I have tried has given me overflow[] or something equally useless.

share|improve this question
Use the undocumented Developer`Kabbalah package. But seriously, there are limits, look at $MaxNumber on your machine. Compare that to what you're trying to generate as an exponent.... – ciao Apr 21 '14 at 21:09
And the exponent 1.1414... is what? An approximation of Sqrt[2], 1 + 14/99, ...? – halirutan Apr 21 '14 at 22:09
@halirutan Just a random number. It was an example. – bwv869 Apr 21 '14 at 22:11
You might try extracting logs once or twice, figuring out what digits you need from that, and exponentiating. Not sure how far one can take this though. – Daniel Lichtblau Apr 22 '14 at 13:57

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