Given a hereditary representation of a number n in base b, let B[b](n) be the nonnegative integer which results if we syntactically replace each b by b + 1 (i.e., B[b] is a base change operator that 'bumps the base' from b up to b + 1). The hereditary representation of 266 in base 2 is 266 | = | 2^8 + 2^3 + 2 | = | 2^(2^(2 + 1)) + 2^(2 + 1) + 2, so bumping the base from 2 to 3 yields B[2](266) = 3^(3^(3 + 1)) + 3^(3 + 1) + 3.

Goodstein's theorem | hereditary representation | Paris-Harrington theorem