User blog:SuperJedi224/Part 1 (Extension)

This is an extension to this post.

New Notations
$$F_{n}^{b}(X)=F_{n}^{b-1}(F_{n}(X));F_{n}^{0}(X)=X$$ (Assumed to be 1 if ommited)

$$F_{n}^{b}(X)\#h=F_{n}^{F_{n}^{b}(X)\#h-1}(X);F_{n}^{b}(X)\#1=F_{n}^{b}(X)$$ (Assumed to be 1 if ommited)

$$F_{n}^{b}(X)\#h\$z=F_{n}^{b}(X)\#(F_{n}^{b}(h)\#z-1)\$z-1;F_{n}^{b}(X)\#h\$1=F_{n}^{b}(X)\#h$$

New Rules
The Grand prefix has been redefined to produce integer values. It is now $$F_{n}^{X+1}(X)$$. The Superior prefix is unchanged.

The Great prefix now represents $$F_{n}(X)\#X$$

"Grandsuperior" gives $$F_{n}^{X+2}(X)$$; and "y-superior" gives $$F_{n}^{y+1}(X)$$

The "Grandsuperior" and "y-superior" compound prefixes are treated as seperate words, while "Grand" and "Superior" are not.

"Great Grand" gives $$F_{n}^{X+1}(X)\#X$$; "Great Grandsuperior" gives $$F_{n}^{X+2}(X)\#X$$; and "Great y-superior" gives $$F_{n}^{y+1}(X)\#X$$

"y-great" gives $$F_{n}(X)\#X\$y$$

"Great" and "y-great" are both treated as seperate words.

Grandeuteroex
The redefined Grandeuteroex is $$F_{1}^{3}(2)$$, or about $$2+2^{1+2^{2.68\times10^{154}}}$$

It is also equal to Bisuperior Deuteroex

Great Deuteroex
The Great Deuteroex is $$F_{1}(2)\#2=F_{1}^{10}(2)=F_{1}(F_{1}(F_{1}(F_{1}(F_{1}(F_{1}(F_{1}(F_{1}(F_{1}(2))))))))))$$

It can be expanded to the following:

$$2+2^{1+2^{2+2^{1+2^{2+2^{1+2^{2+2^{1+2^{2+2^{1+2^{2+2^{1+2^{2+2^{1+2^{2+2^{1+2^{2+2^{1+2^{2+2^{1+2^{1}}}}}}}}}}}}}}}}}}}}$$

Great Grandeuteroex
$$F_{1}^{3}(2)\#2=F_{1}^{F_{1}^{3}(2)}(2)=F_{1}^{Grandeuteroex}(2)$$ That means its the grandeuteroexth term in a sequence where the zeroth term is two and each following term is F1 of the previous term.

Trigreat Decasuperior Googoloex
I have no idea just how big this is, but it's consistent with the naming rules. It is equal to $$F_{1}^{11}(10^{100})\#10^{100}\$3$$