Left-Reverse Factorial Notation

Left-Reverse Factorial Notation is a notation coined by Googology Wiki user AblanGG.Kerem's Numbers - Left-Reverse Factorial Notation. Retrieved UTC 2023-08-10 05:27.Kerem's Numbers - Left-Reverse Factorial Notation. Retrieved UTC 2023-08-10 05:45. Kerem's Numbers - Left-Reverse Factorial Notation. Retrieved UTC 2023-08-10 15:50. This notation is ill-defined by the same reason in Right-Reverse Factorial Notation.
== Definition ==
=== Original version ===
Here is a copy of the original source:
\(n,m,j \in \mathbb{R}, z,l \in \mathbb{N}\)
For k and K , please look at Kerem's Number.
n! = nxn-1x....2x1
n¡= (n!xn-1!xn-2!....2!x1)^(n!xn-1!xn-2!...2!x1)^.......^(n!xn-1!xn-2!x.....x1) it has n!xn-1!x....2!x1 amount of power tower 
n¡¡¡...(z amount of ¡'s)...¡¡^m means that if you want to write without (^m) [n¡¡¡....¡¡¡] than you have to write (z!xz-1!...1!)^(z!xz-1!...1!)^.......^(z!xz-1!...1) (m amount of power tower) amount of ¡'s next to n
¡n¡¡¡...(z amount of ¡'s)...¡^m means that if you want to write without (^m) [¡n¡¡¡...¡¡¡] then you have to write (z!xz-1!...1!)^(z!xz-1!...1!)^.......^(z!xz-1!...1) (m amount of power tower) amount of ¡'s right next to ¡n. And if you want to write without the left ¡ [n¡¡¡...¡¡¡] then you have to write (K!xK-1!...1!)^(K!xK-1!....1!)^(K!xK-1!...)^...^(K!xK-1!....1!) (K amount of power tower) amount of ¡'s right next to n.
¡¡¡...(l amount of ¡'s)...¡¡¡n¡¡¡...(z amount of ¡'s)...¡^m means that if you want to write without (^m) [¡¡¡...(l amount of ¡'s)...¡¡¡n¡¡¡...¡¡¡] then you have to write (z!xz-1!...1!)^(z!xz-1!...1!)^.......^(z!xz-1!...1) (m amount of power tower) amount of ¡'s right next to ¡¡¡...(l amount of ¡'s)...¡¡¡n. And if you want to write without the left ¡'s [n¡¡¡...¡¡¡] then you have to write (kkk...(l amount of)...kK !x kkk...(l amount of)...kK -1!....1!)^(kkk...(l amount of)...kK !x kkk...(l amount of)...kK -1!....1!)^...^(kkk...(l amount of)...kK !x kkk...(l amount of)...kK -1!....1!) [it has (kkk...(l amount of)...kK !x kkk...(l amount of)...kK -1!....1!) amount of power tower.] amount of ¡¡¡...¡¡¡'s right next to n¡¡¡...¡¡¡.
j^¡¡¡...(l amount of ¡'s)...¡¡¡n¡¡¡...(z amount of ¡'s)...¡¡¡^m means that you want to write without (^m) [j^¡¡¡...(l amount of ¡'s)...¡¡¡n¡¡¡...¡¡¡] then you have to write (z!xz-1!...1!)^(z!xz-1!...1!)^.......^(z!xz-1!...1) (m amount of power tower) amount of ¡'s next to j^¡¡¡...(l amount of ¡'s)...¡¡¡n. And if you want to write without (j^) then you have to write (kkk...(j amount of)...kK !x kkk...(j amount of)...kK -1!....1!)^(kkk...(j amount of)...kK !x kkk...(j amount of)...kK -1!....1!)^...^(kkk...(j amount of)...kK !x kkk...(j amount of)...kK -1!....1!) [it has (kkk...(j amount of)...kK !x kkk...(j amount of)...kK -1!....1!) amount of power tower.] amount of ¡¡¡...(l amount of ¡'s)...¡¡¡'s left next to n¡¡¡...¡¡¡
=== Second version ===
Here is a copy of the updated source:
\(n,m,j \in \mathbb{R}, z,l \in \mathbb{N}\)
For k and K , please look at Kerem's Number.
n! = nxn-1x....2x1
n¡= (n!xn-1!xn-2!....2!x1)^(n!xn-1!xn-2!...2!x1)^.......^(n!xn-1!xn-2!x.....x1) it has n!xn-1!x....2!x1 amount of power tower 
n¡¡¡...(z amount of ¡'s)...¡¡^m means that if you want to write without (^m) [n¡¡¡....¡¡¡] than you have to write (z!xz-1!...1!)^(z!xz-1!...1!)^.......^(z!xz-1!...1) (m amount of power tower) amount of ¡'s next to n
¡n¡¡¡...(z amount of ¡'s)...¡^m means that if you want to write without (^m) [¡n¡¡¡...¡¡¡] then you have to write (z!xz-1!...1!)^(z!xz-1!...1!)^.......^(z!xz-1!...1) (m amount of power tower) amount of ¡'s right next to ¡n. And if you want to write without the left ¡ [n¡¡¡...¡¡¡] then you have to write (K!xK-1!...1!)^(K!xK-1!....1!)^(K!xK-1!...)^...^(K!xK-1!....1!) (K amount of power tower) amount of ¡¡¡...¡¡¡'s right next to n.
¡¡¡...(l amount of ¡'s)...¡¡¡n¡¡¡...(z amount of ¡'s)...¡^m means that if you want to write without (^m) [¡¡¡...(l amount of ¡'s)...¡¡¡n¡¡¡...¡¡¡] then you have to write (z!xz-1!...1!)^(z!xz-1!...1!)^.......^(z!xz-1!...1) (m amount of power tower) amount of ¡'s right next to ¡¡¡...(l amount of ¡'s)...¡¡¡n. And if you want to write without the left ¡'s [n¡¡¡...¡¡¡] then you have to write (kkk...(l amount of)...kK !x kkk...(l amount of)...kK -1!....1!)^(kkk...(l amount of)...kK !x kkk...(l amount of)...kK -1!....1!)^...^(kkk...(l amount of)...kK !x kkk...(l amount of)...kK -1!....1!) [it has (kkk...(l amount of)...kK !x kkk...(l amount of)...kK -1!....1!) amount of power tower.] amount of ¡¡¡...¡¡¡'s right next to n¡¡¡...¡¡¡.
j^¡¡¡...(l amount of ¡'s)...¡¡¡n¡¡¡...(z amount of ¡'s)...¡¡¡^m means that you want to write without (^m) [j^¡¡¡...(l amount of ¡'s)...¡¡¡n¡¡¡...¡¡¡] then you have to write (z!xz-1!...1!)^(z!xz-1!...1!)^.......^(z!xz-1!...1) (m amount of power tower) amount of ¡'s next to j^¡¡¡...(l amount of ¡'s)...¡¡¡n. And if you want to write without (j^) then you have to write (kkk...(j amount of)...kK !x kkk...(j amount of)...kK -1!....1!)^(kkk...(j amount of)...kK !x kkk...(j amount of)...kK -1!....1!)^...^(kkk...(j amount of)...kK !x kkk...(j amount of)...kK -1!....1!) [it has (kkk...(j amount of)...kK !x kkk...(j amount of)...kK -1!....1!) amount of power tower.] amount of ¡¡¡...(l amount of ¡'s)...¡¡¡'s left next to n¡¡¡...¡¡¡
=== Third version ===
Here is a copy of the updated source:
\(n,m,j,z,l \in \mathbb{N}+\) 
For k and K , please look at Kerem's Number.
n! = nxn-1x....2x1
n¡= (n!xn-1!xn-2!....x1)^(n!xn-1!xn-2!...x1)^.......^(n!xn-1!xn-2!x.....x1) it has n!xn-1!x....x1 amount of power tower 
Example 1: 13¡ = (13!x12!x11!x....2!x1!)^(13!x12!x11!x....2!x1!)^....^(13!x12!x11!x....2!x1!) it has 13!x12!x11!x....2!x1! amount of power tower.
Example 2: 1¡ = (1!)^(1!) it has 1! amount of power tower.
n¡¡¡...(z amount of ¡'s)...¡¡^m means that if you want to write without (^m) [n¡¡¡....¡¡¡] than you have to write (z!xz-1!...1!)^(z!xz-1!...1!)^.......^(z!xz-1!...1) (m amount of power tower) amount of ¡'s next to n
¡n¡¡¡...(z amount of ¡'s)...¡^m means that if you want to write without (^m) [¡n¡¡¡...¡¡¡] then you have to write (z!xz-1!...1!)^(z!xz-1!...1!)^.......^(z!xz-1!...1) (m amount of power tower) amount of ¡'s right next to ¡n. And if you want to write without the left ¡ [n¡¡¡...¡¡¡] then you have to write (K!xK-1!...1!)^(K!xK-1!....1!)^(K!xK-1!...)^...^(K!xK-1!....1!) (K amount of power tower) amount of ¡¡¡...¡¡¡'s right next to n.
¡¡¡...(l amount of ¡'s)...¡¡¡n¡¡¡...(z amount of ¡'s)...¡^m means that if you want to write without (^m) [¡¡¡...(l amount of ¡'s)...¡¡¡n¡¡¡...¡¡¡] then you have to write (z!xz-1!...1!)^(z!xz-1!...1!)^.......^(z!xz-1!...1) (m amount of power tower) amount of ¡'s right next to ¡¡¡...(l amount of ¡'s)...¡¡¡n. And if you want to write without the left ¡'s [n¡¡¡...¡¡¡] then you have to write (kkk...(l amount of)...kK !x kkk...(l amount of)...kK -1!....1!)^(kkk...(l amount of)...kK !x kkk...(l amount of)...kK -1!....1!)^...^(kkk...(l amount of)...kK !x kkk...(l amount of)...kK -1!....1!) [it has (kkk...(l amount of)...kK !x kkk...(l amount of)...kK -1!....1!) amount of power tower.] amount of ¡¡¡...¡¡¡'s right next to n¡¡¡...¡¡¡.
j^¡¡¡...(l amount of ¡'s)...¡¡¡n¡¡¡...(z amount of ¡'s)...¡¡¡^m means that you want to write without (^m) [j^¡¡¡...(l amount of ¡'s)...¡¡¡n¡¡¡...¡¡¡] then you have to write (z!xz-1!...1!)^(z!xz-1!...1!)^.......^(z!xz-1!...1) (m amount of power tower) amount of ¡'s next to j^¡¡¡...(l amount of ¡'s)...¡¡¡n. And if you want to write without (j^) then you have to write (kkk...(j amount of)...kK !x kkk...(j amount of)...kK -1!....1!)^(kkk...(j amount of)...kK !x kkk...(j amount of)...kK -1!....1!)^...^(kkk...(j amount of)...kK !x kkk...(j amount of)...kK -1!....1!) [it has (kkk...(j amount of)...kK !x kkk...(j amount of)...kK -1!....1!) amount of power tower.] amount of ¡¡¡...(l amount of ¡'s)...¡¡¡'s left next to n¡¡¡...¡¡¡
==Sources==
Category:Factorials
Category:Notations
Category:Unformalised