## FANDOM

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Let me introduce the function based on factorial (!). I will call this function Super Staging Factorial Function. In this function we can go far beyond with the simple notation !. I gonna tell how I got this idea. I mainly got this inspiration by dysfunctionalfactorial's idea at http://www.artofproblemsolving.com/community/c1664h1003843 about factorial. This is not be confused with Faxul terms. The naming system focuses with the number 200, similar to Faxul terms. I use Faxul terms to see how fast this function grow perspective. I don't think this function would beat Expofaxul terms very fast. Numbers I have created is based on the name Lexol, meaning "Level Factorial", the first tier. And name Raxol, meaning "Rank Factorial", the second tier. I hasn't gotten to the third yet. We'll use pairs of vertical pipes (|) with number or chain ($$α$$) within those pairs of pipes, and a number in the subscript ($$β$$) outside the pipes, (AND if necessery, have a number superscript ($$γ$$) which describes the repeat of the function), and aswell as a input ($$x$$) to make those process:

$$|α|_β^γ(x)=output$$

Let's clearify some rules:

• Rule 1: numbers in the function must be intergers that are 1 or greater.
• Rule 2: $$|1|_1(x)=x!$$
• Rule 3: $$|m|_n^1(x)=|m|_n(x)$$
• Rule 4: $$|m|_n^{o+1} (x)=|m|_n^o(|m|_n^1(x))$$
• Rule 5: $$|m|_{n+1} ^1(x)=|m|_n^x(x)$$
• Rule 6: $$|m+1|_1(x)=|m|_x(x)$$
• Rule 7: $$|...|1|...(\text{n+1 pairs of |'s})...|_1(x) = |...|x|...(\text{n pairs of |'s})...|_1(x)$$
• Rule 1,3-6 is also applied on multiple |'s
• Rule 8: $$|...|m|... (\text{n pairs of |'s}) ...|_1(x) = |n,m|_1(x)$$
• Rule 9: $$|m+1,1_1,1_2,...,1_(n+1) |_1(x)=|m,x,1_1,1_2,...,1_n|_1(x)$$

Examples:

• $$|1|_1(3)=3!=3·2·1=6$$
• $$|1|_1(10)=10!=3.628.800$$
• $$|1|_1(100)=100!≈9,33262154439·10^{157}$$
• $$|1|_1(200)=200!≈7,9·10^{375}$$, I name this number Lexol. Also equal to Faxul.
• $$|1|_1(|1|_1(3))=(3!)!=720$$, this can be compressed into $$|1|_1^2(3)$$.
• $$|1|_1^2(10)=(10!)!≈5,2279·10^{22228109}$$
• $$|1|_1^2(200)=(200!)!≈10^{9,48539·10^378}$$, which is named Kilolexol.

More names:

• Megalexol
• Gigalexol
• Dialexol
• Trialexol
• Grand Lexol
• Bigrand Lexol
• Ultimate Lexol
• Uldimate Lexol
• Raxol = $$|1|1|_1(200) = |200_1,200_2,...,200_{200}|_1(200)$$