User blog:Xtrasnack/The paradox function.

I got an idea from numbers like BIG FOOT and Rayo's number diagonalizing over formal systems, so I came up with this function:

Paradox(n) = The result if you input n into the fastest growing function whose totality is provable in Peano Arithmitic and who can be described with at most n symobols in Typographical Number Theory, with the modification that n can be used as a single symbol.

Note: The wikipedia website for Typographical Number Theory is not completely accurate, and further information can be found in Godel Esher Bach, where it was originaly described.

I define Xtrasnack's paradox number as Paradox1000(10100) where fnrepresents f(f(f(f(... with n fs.