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I remember reading in RPF's biographical book, "Surely you're joking Mr. Feynman" that he used to have timed contest about writing down the biggest number using standard symbols.

Instead of the time restriction, I was wondering what if we restrict the number of characters, to say $N=10$. What is the largest number we can write using $N$ characters using numbers and standard functions known to most mathematicians? Of course I think the real difficulty would be in proving the said number is the largest. What is the largest number you can think of with $N=10$?

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    Everything hinges on what you mean by "standard functions known to most mathematicians," as well as what characters you're allowing (do parentheses count extra?) and what shorthand you're allowing. If B is valid shorthand for the busy beaver function then I think it will be hard to beat BBBBBBBBB9. This number is pointlessly large.2010-11-27
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    Scott Aaronson has written an entertaining essay on this very subject: [Who Can Name the Bigger Number?](http://www.scottaaronson.com/writings/bignumbers.html)2010-11-27
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    If you kept the range of allowed functions very small, it could be an interesting exercise. Say only absolute basic operators, brackets allowed free, as I don't see why order of operator precedence should interfere as that is essentially arbitary: +, -, *, /, ln, e, i. Perhaps allowing ln to be counted as a single character, abbreviated as l - the inclusion of **i** is not strictly necessary as it can be built (-1)^(1/2), and I omitted any root for the same reason, but it's sort of elementary.2010-11-27

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