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