Another rapidly growing function is the Smorynski function, which also maps N2 to N. The

Chapter 5, Problem 43

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Another rapidly growing function is the Smorynski function, which also maps N2 to N. The definition is S(0, n) = nn for all n [ N S(m, n) = S(m 1, S(m 1, n)) for all m [ N, n [ N, m > 0 a. How does S(0, n) compare to A(0, n)? (See Exercise 40.) b. Find (show all steps) an expression for the value of S(1, n). c. A googolplex is a very large number, which if written in standard form (such as 1,000,000 ), even in 1-point font, would take more room to write than the diameter of the known universe. Look up the definition of the googolplex and write it as S(m, n) for a specific value of m and n.