Rayo's number is one of the largest named numbers, coined in a large number battle pitting Agustín Rayo against Adam Elga.[1][2] Rayo's number is, in Rayo's own words, "the smallest positive integer bigger than any finite positive integer named by an expression in the language of first order set theory with a googol symbols or less."
By letting the number of symbols range over the natural numbers, we get a very quickly growing function Rayo(n)Rayo(n) (alternatively expressed as FOST(n)FOST(n)[3]). Rayo's number is Rayo(10100)Rayo(10100). Rayo's function is uncomputable, which means that it is impossible for a Turing machine (and, by the Church–Turing thesis, any modern computer) to calculate Rayo(n)Rayo(n). Rayo's function is one of the fastest growing functions ever to arise in professional mathematics[citation needed]; only a few functions, especially its generalization, the FOOT (first-order oodle theory) function surpass it in strength.
(Thanks Wikipedia)