It is actually no stronger than Bowers' multi-variable arrays. Can we reach \(f_{\omega^\omega}(n)\)-growing function with finitely many variables? Ikosarakt1 (talk ^ contribs) 14:40, October 17, 2013 (UTC)

- It doesn't reach \(f_{\omega^\omega}(n)\) with finitely many variables, but it reaches \(f_{\omega^\omega}(n)\) when the numbers of variables is made variable, as shown in the calculation. Kyodaisuu (talk) 15:17, October 17, 2013 (UTC)

Welcome to Googology Wiki, Kyodaisuu! It's good to add new entries, however I must say that Taro's function is not new. There are references to this function on sci.math since back in the 1990's, and of course a similar version can be made by taking defining \(A(a_n,a_{n-1},\ldots,a_0,n) = f_{\omega^n * a_n + \omega^{n-1} * a_{n-1} + \ldots + a_0}(n)\), and the FGH is quite old. Deedlit11 (talk) 14:45, October 17, 2013 (UTC)

- I don't know the similar version that you mention. Please add the reference in the entry. Kyodaisuu (talk) 15:17, October 17, 2013 (UTC)

None of the rules for three-entry arrays refer to two-entry arrays. you're.so.pretty! 01:19, July 26, 2014 (UTC)

- X and Y are meant to be sequences of entries of any length, including 0. Deedlit11 (talk) 02:48, July 26, 2014 (UTC)

- There is no rule of explicitly shorten the length of the array gradually, but as the rule of A(Y,a) = a+1 exists, left part of Y will be finally cut off, and A(Y,X,a) = A(X,a) is satisfied. Therefore, the relationship A(Y,X,a) = A(X,a) is derived from this definition. Kyodaisuu (talk) 03:25, July 26, 2014 (UTC)

I made a similar extended Ackermann function. # means the rest.

A(0,#) = A(#)

A(x) = x+1

A(#,x,0,0,...,0,0) = A(#,x-1,1,1,...,1,1)

A(#,x,0,0,...,0,0,y) = A(#,x-1,y,y,...,y,y,y)

A(#,x,y) = A(#,x-1,A(#,x,y-1))

ALSO, did you realize that a user under the name " bimbow" made the User blog:B1mb0w/Deeply Nested Ackermann based on his Modified Ackermann function?

Do you know what TMAF, Deeply Nested Ackermann, and my function have in common?

(HINT: it's quite obvious :))

Oh that was me. I forgot to sign my post. 99.185.0.100 18:59, August 5, 2015 (UTC)