Category:Definitions/Ackermann Functions

This category contains definitions related to Ackermann Functions.
Related results can be found in Category:Ackermann Functions.

The Ackermann-Péter function $A: \Z_{\ge 0} \times \Z_{\ge 0} \to \Z_{> 0}$ is an integer-valued function defined on the set of ordered pairs of positive integers as:

$\map A {x, y} = \begin{cases} y + 1 & : x = 0 \\

\map A {x - 1, 1} & : x > 0, y = 0 \\ \map A {x - 1, \map A {x, y - 1} } & : \text{otherwise} \end{cases}$