## What is the largest computable number expressable in 10 unicode characters? [closed]

I'm running an informal contest right now, the "who can name the biggest number" contest. The rules are that you can only use 10 unicode characters and "accepted mathematical notation" (functions, constants, and other notational devices defined in peer-reviewed mathematical publications), and that a mathematician with an encyclopedic knowledge of mathematical publications on a desert island should be able to program a Turing machine to compute the value in your entry in a finite number of steps using only the information in those ten characters. Some of the ideas include:

A(g!!,g!!)


where A is the Ackermann Function and g is Graham's number

g→g→g→g→g!


where → means the Conway chained arrow notation and g is again Graham's number. As you can see, some additional text is allowed to provide context or pointers to the relevant publications, but this text isn't allowed to introduce new definitions.

Anyway, my question is, are there yet larger numbers that satisfy the rules of the contest?

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Needless to say, it depends on what qualify as “accepted mathematical notation.” – Tsuyoshi Ito Aug 4 2010 at 1:47
Your question isn't well-posed. And your examples use more than 10 characters. This seems more entertainment than a research-level question. If you had a table of "accepted mathematical notation", an answer would amount to a simple search through a space of allowable expressions for the max value. – Ryan Budney Aug 4 2010 at 1:50
@Ryan: “And your examples use more than 10 characters.” You have keen eyes. – Tsuyoshi Ito Aug 4 2010 at 1:55
For lulz...how about $TREE(9\uparrow ^9 9)$: en.wikipedia.org/wiki/… – Steve Huntsman Aug 4 2010 at 2:26
Thor -- so before participating in this game one should study all peer-reviewed publications? – algori Aug 4 2010 at 3:21