Definition:Ackermann Function/Mistake 1

Source Work

 * The Dictionary
 * $65,536$
 * $65,536$

Mistake

 * The Ackermann function is one of the fastest increasing functions used in mathematics. Its values from $\map f 0$ to $\map f 5$ are $1$, $3$, $4$, $8$, $65,536$.

Correction
First note that this should read:
 * Its values from $\map f 0$ to $\map f 4$ are $1$, $3$, $4$, $8$, $65,536$.

Next it should be noted that has at this stage not specified what is meant by the Ackermann function. When later in he does define it, he does so as a function of $2$ variables.

It is probable that he was referring to the function:
 * $\map f n = \map {H_n} {2, n}$

where $H_n$ is the $n$th hyperoperation, defined as:

$\map {H_n} {x, y} = \begin{cases} y + 1 & : n = 0 \\ x & : n = 1, y = 0 \\ 0 & : n = 2, y = 0 \\ 1 & : n > 2, y = 0 \\ \map {H_{n - 1} } {x, \map {H_n} {x, y - 1} } & : n > 0, y > 0 \end{cases}$

This leads to the results: