Find these values of Ackermann's function. a) A(2, 3) *b)

Step 1 of 3

The Ackermann’s function is defined by

\(A(m, n)=\left\{\begin{array}{ll}
2 n, & \text { If } m=0 \\
0, & \text { If } m \geq 1 \text { and } n=0 \\
2, & \text { If } m \geq 1 \text { and } n=1 \\
A(m-1, A(m, n-1)), & \text { If } m \geq 1 \text { and } n \geq 2
\end{array}\right.\)

(a) To find \(A(2,3)\)

Here,

\(\begin{aligned}
m & =2>1 \\
n & =3>2
\end{aligned}\)

Therefore, from the definition of Ackermann’s function,

\(\begin{aligned}
A(2,3) & =A(2-1, A(2,3-1)) \\
& =A(1, A(2,2))
\end{aligned}\)