Manuals/calci/ACKERMANN

ACKERMANN(m,n)

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} are the positive integers.

Description

• The Ackermann function is a classic example of a recursive function, notable especially because it is not a primitive recursive function.
• All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive.
• Its arguments are never negative and it always terminates.
• The two-argument Ackermann–Péter function, is defined as follows:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A(m,n) = \begin{cases} n+1 \mbox {if} m=0 \\ A(m-1,1) & \mbox {if} m>0 and n=0 \\ A(m-1,A(m,n-1))& \mbox {if} m>0 and n>0 \end{cases} } \\

for nonnegative integers m and n.

• Its value grows rapidly, even for small inputs.

See Also

• List of Main Z Functions

• Z3 home