User blog comment:VoidSansXD/Multiple Array Notation/@comment-35470197-20190315001356

> (a)(x) = f_x(a) (I think).

I guess that you skipped a recursion because you only understand the definitions of \(f_0,f_1,f_2.f_3\). Even if you could not understand what \(f_x\) means, then you can learn it now. If you skip any intermediate descriptions, then you can state \((a)(x) = f_{\varepsilon_0[x]}(a)\) for \(x > 2\). It is non-sense.

Ignoring the lack of knowledge causes no progression. It is good for you to define \(f_5\) explicitly. Learning in a step-by-step way is one direct solution to go further in googology. Otherwise, you will never understand what \(f_{\omega}\) actually means. The same advice is applicable to your other blog posts.

Or you might not understand what "definition" is. Then learn how to define stuffs from articles and blog posts.