Category:Ackermann Functions

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This category contains results about Ackermann Functions.
Definitions specific to this category can be found in Definitions/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:

$A \left({x, y}\right) = \begin{cases} y + 1 & : x = 0 \\ A \left({x - 1, 1}\right) & : x > 0, y = 0 \\ A \left({x - 1, A \left({x, y - 1}\right)}\right) & : \text{otherwise} \end{cases}$

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