Rayo's number

Rayo's number is an incredibly enormous (and possibly infinite) number that was created during a large number battle pitting Agust&iacute;n Rayo against Adam Elga.

Duel
Rayo and Elga's number duel was based on an article by Scott Aaronson.

Definition
Rayo's number is, in Rayo's own words, "the smallest number bigger than any finite number named by an expression in the language of set theory with a googol symbols or less."