Note

= Notation 1 =
{x,x(L(x,L(1,2)2))2}
{x,x(L(L(2))2}={x,x(L,x(L,x(…(L,x)…)2)2)2} by x nests
This notation is defined in 2023. Work in progress.
==Approximations==
\begin{array}{lcl}\{n,n\} = n^n \\ \{n,n,n\} = n\uparrow^{n}n \\ \{n,\{2\}\} = \{n,n(1)2\} \\ \{n,\{3\}\} = \{n,n(1)3\} \\ \{n,\{n\}\} = \{n,n(1)n\} \\ \{n,\{n,\{2\}\}\} = \{n,n(1)(1)2\} \\ \{n,\{n\},\{2\}\} = \{n,n(2)2\} \\ \{n\{n\}\} = \{n,n(0,1)2\} \\ \{n\{n\{n\}\}\} = \{n,n(0,0,1)2\} \\ \{n,n/2\} = \{n,n((1)1)\} \\ \{n,n/3\} = \{n,n(((1)1)1)2\} \\ \{n,n/n\} = X\uparrow\uparrow X \And n \\ \{n,n/n/2\} = X\uparrow^{3}X\And n \\ \{n,n//2\} = \{X,X,X\}\And n \\ \{n,n/_22\} = \{X,X(1)2\}\And n \\ \{n,n/_{1,2}2\} = \{X,X(1)X\}\And n\end{array}
== Numbers ==
Googol = {10,100}
Gossol = {10,{100}}
Tritri = {3,3,3}
Centillion = {10,303}
Noom = {10,10(L(1)2)2}
= Notation 2 =
\begin{array}{lcl}i(x) = x + 1 \\ i(x,2) = i^{x}(x) \\ i(x,3) = i^{x}(x,2) \\ i(x,m) = i^{x}(x,m-1) \\ i(x,x) = i^{x}(x,x-1) \\ i(x,x,2) > \{x,x,x,2\} \\ i(x,x,x) > \{x,x,x,x\} \\ i(x,x\{1\}2) > \{x,x+1(1)2\} \end{array}