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- and are the positive integers.
- 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:
for nonnegative integers m and n.
- Its value grows rapidly, even for small inputs.