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)


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.

The "Omega" prefix yields F_{n}(X)\#1\$X, and "Omegreat" yields F_{n}(X)\#X\$X. These are both treated as seperate words.

Some Numbers


The redefined Grandeuteroex is F_{1}^{3}(2), or about 2^{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:


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^{300}

Omegreat Grandgoogoloex

Another incredibly large one. This one is equal to F_{1}^{10^{100}+1}(10^{100})\#10^{100}\$10^{100}

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