User:Googleaarex/Extended Up-Arrow Notation/Nested

Nested Up-Arrow Notation is 2nd part of Extended Up-arrow Notation series.

Arrows inside Arrow Types
Let \(a \uparrow_{\uparrow_2} b = a \uparrow_{b} a\) and has growth rate \(\omega^\omega\)

Then \(a \uparrow_{\uparrow_2}\uparrow b = \underbrace{a \uparrow_{a \uparrow_{... a \uparrow_{a} a ...} a} a}_{b}\), \(a \uparrow_{\uparrow_2}\uparrow\uparrow b = \underbrace{a \uparrow_{a \uparrow_{... a \uparrow_{a} a ...} a} a}_{\underbrace{a \uparrow_{a \uparrow_{... a \uparrow_{a} a ...} a} a}_{... \underbrace{a \uparrow_{a \uparrow_{... a \uparrow_{a} a ...} a} a}_{a} ...}}\) (with b braces), etc.