Question 177
The function $f(x, y)$, defined on the set of all nonnegative integers, satisfies
(i) $f(0, y) = y + 1$,
(ii) $f(x + 1, 0) = f(x, 1)$, and
(iii) $f(x + 1, y + 1) = f(x, f(x + 1, y))$.
Find (a) $f(3, 2005)$, and (b) $f(4, 2005)$.
(i) $f(0, y) = y + 1$,
(ii) $f(x + 1, 0) = f(x, 1)$, and
(iii) $f(x + 1, y + 1) = f(x, f(x + 1, y))$.
Find (a) $f(3, 2005)$, and (b) $f(4, 2005)$.