Interesting article on big (finite) numbers that have practical or theoretical relevance beyond just being gargantuan.
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You have fifteen seconds. Using standard math notation, English words, or both, name a single whole number—not an infinity—on a blank index card. Be precise enough for any reasonable modern mathematician to determine exactly what number you’ve named, by consulting only your card and, if necessary, the published literature.
So contestants can’t say "the number of sand grains in the Sahara," because sand drifts in and out of the Sahara regularly. Nor can they say "my opponent’s number plus one," or "the biggest number anyone’s ever thought of plus one"—again, these are ill-defined, given what our reasonable mathematician has available. Within the rules, the contestant who names the bigger number wins.
Are you ready? Get set. Go.
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http://www.scottaaronson.com/writings/bignumbers.html