User blog:Ynought/Hyper extended array hierarchy

here i will be extending my array hierarchy.

If you haven’t seen or read the previous posts here they are:

https://googology.wikia.com/wiki/User_blog:Ynought/Array_hierarchy

https://googology.wikia.com/wiki/User_blog:Ynought/Extended_array_hierarchy

Here \(\bullet\) will be anything that is already well defined at that point

so:

\(\bullet\leftarrow_0=\bullet_{\bullet_{\bullet_{\dots_\bullet}}}^{\bullet^{\bullet^{\dots^{\bullet}}}}\)

when x is some number bigger than 0:

here \(Q=\bullet_{\bullet\leftarrow_{x-1}}^{\bullet\leftarrow_{x-1}}\leftarrow_{x-1}\)

\(\bullet\leftarrow_x=\bullet_{Q_{Q_{\dots_{Q}}}}^{Q^{\dots^Q}}\leftarrow_{x-1}\)

Here \(E=(10...,10)_{(10...,10)}^{(10...,10)}\leftarrow_{(10…,10)}\) with 10 10s

and \(E_0=E\)

and \(E_k=\)

\((E_{k-1}...,E_{k-1})_{(E_{k-1}...,E_{k-1})}^{(E_{k-1}...,E_{k-1})}\leftarrow_{(a+E_{a-1},b+E_{b-1}...,c-1)}\) where in all the array except the one here \(\leftarrow_{(a,b...,c)}\) has 10 \(E_{k-1}\)'s

\(\bullet\leftarrow_{(a,b…,c)}=\bullet\leftarrow_{(a+E_a,b+E_b...,c-1)}\)

here every variables in every single \(\bullet\)gets replaced with \(\bullet\leftarrow_{(a+c,b+c…,c-1)}\)

\(\bullet\leftarrow_{\bullet_2}^1\)

\(=\bullet_{E_{\bullet}}^{E_{\bullet}}\leftarrow_{E_{\bullet}}\dots\leftarrow_{E_{\bullet}}\) with \(\bullet\leftarrow_{\bullet_2}\) \(\leftarrow_{E_{(\bullet)}}\)’s