User blog comment:Emlightened/Intro/@comment-1605058-20160109180510/@comment-1605058-20160109211045

Almost all functions I can think of can be defined in this way, including busy beaver function, Rayo's function or FOOT function. Take a look at the first one: it's definition is "the largest number which is an output of n-state Turing machine". It doesn't refer to any other functions.