Left-Reverse Factorial Notation

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This is an article which refers to a personal web site as the first source of the notion in the title. Please be careful as a personal web site is not usually a peer-reviewed source unlike academic journals, and hence might include wrong information. For more details, see this document.

This is an article on a googological notion whose definition is frequently updated, especially when this article points out issues in the definition. Therefore, the specific issues explained in this article might not be applicable to the current definition. This does not mean that the current definition has no issues, as editors in this wiki do not have a duty to chase all updates and verify all changes in such a frequently updated work, which requires heavy maintenance.

Left-Reverse Factorial Notation is a notation coined by Googology Wiki user AblanGG.^[1]^[2] ^[3] 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:^[1]

\(n,m,j \in \mathbb{R}, z,l \in \mathbb{N}\) 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 (k_{k_{k_{...(l amount of)..._{k_K}}}} !x k_{k_{k_{...(l amount of)..._{k_K}}}} -1!....1!)^(k_{k_{k_{...(l amount of)..._{k_K}}}} !x k_{k_{k_{...(l amount of)..._{k_K}}}} -1!....1!)^...^(k_{k_{k_{...(l amount of)..._{k_K}}}} !x k_{k_{k_{...(l amount of)..._{k_K}}}} -1!....1!) [it has (k_{k_{k_{...(l amount of)..._{k_K}}}} !x k_{k_{k_{...(l amount of)..._{k_K}}}} -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 (k_{k_{k_{...(j amount of)..._{k_K}}}} !x k_{k_{k_{...(j amount of)..._{k_K}}}} -1!....1!)^(k_{k_{k_{...(j amount of)..._{k_K}}}} !x k_{k_{k_{...(j amount of)..._{k_K}}}} -1!....1!)^...^(k_{k_{k_{...(j amount of)..._{k_K}}}} !x k_{k_{k_{...(j amount of)..._{k_K}}}} -1!....1!) [it has (k_{k_{k_{...(j amount of)..._{k_K}}}} !x k_{k_{k_{...(j amount of)..._{k_K}}}} -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:^[2]

\(n,m,j \in \mathbb{R}, z,l \in \mathbb{N}\) 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 (k_{k_{k_{...(l amount of)..._{k_K}}}} !x k_{k_{k_{...(l amount of)..._{k_K}}}} -1!....1!)^(k_{k_{k_{...(l amount of)..._{k_K}}}} !x k_{k_{k_{...(l amount of)..._{k_K}}}} -1!....1!)^...^(k_{k_{k_{...(l amount of)..._{k_K}}}} !x k_{k_{k_{...(l amount of)..._{k_K}}}} -1!....1!) [it has (k_{k_{k_{...(l amount of)..._{k_K}}}} !x k_{k_{k_{...(l amount of)..._{k_K}}}} -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 (k_{k_{k_{...(j amount of)..._{k_K}}}} !x k_{k_{k_{...(j amount of)..._{k_K}}}} -1!....1!)^(k_{k_{k_{...(j amount of)..._{k_K}}}} !x k_{k_{k_{...(j amount of)..._{k_K}}}} -1!....1!)^...^(k_{k_{k_{...(j amount of)..._{k_K}}}} !x k_{k_{k_{...(j amount of)..._{k_K}}}} -1!....1!) [it has (k_{k_{k_{...(j amount of)..._{k_K}}}} !x k_{k_{k_{...(j amount of)..._{k_K}}}} -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:^[3]

\(n,m,j,z,l \in \mathbb{N}+\) 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 (k_{k_{k_{...(l amount of)..._{k_K}}}} !x k_{k_{k_{...(l amount of)..._{k_K}}}} -1!....1!)^(k_{k_{k_{...(l amount of)..._{k_K}}}} !x k_{k_{k_{...(l amount of)..._{k_K}}}} -1!....1!)^...^(k_{k_{k_{...(l amount of)..._{k_K}}}} !x k_{k_{k_{...(l amount of)..._{k_K}}}} -1!....1!) [it has (k_{k_{k_{...(l amount of)..._{k_K}}}} !x k_{k_{k_{...(l amount of)..._{k_K}}}} -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 (k_{k_{k_{...(j amount of)..._{k_K}}}} !x k_{k_{k_{...(j amount of)..._{k_K}}}} -1!....1!)^(k_{k_{k_{...(j amount of)..._{k_K}}}} !x k_{k_{k_{...(j amount of)..._{k_K}}}} -1!....1!)^...^(k_{k_{k_{...(j amount of)..._{k_K}}}} !x k_{k_{k_{...(j amount of)..._{k_K}}}} -1!....1!) [it has (k_{k_{k_{...(j amount of)..._{k_K}}}} !x k_{k_{k_{...(j amount of)..._{k_K}}}} -1!....1!) amount of power tower.] amount of ¡¡¡...(l amount of ¡'s)...¡¡¡'s left next to n¡¡¡...¡¡¡

Sources[]

↑ ^1.0 ^1.1 Kerem's Numbers - Left-Reverse Factorial Notation. Retrieved UTC 2023-08-10 05:27.
↑ ^2.0 ^2.1 Kerem's Numbers - Left-Reverse Factorial Notation. Retrieved UTC 2023-08-10 05:45.
↑ ^3.0 ^3.1 Kerem's Numbers - Left-Reverse Factorial Notation. Retrieved UTC 2023-08-10 15:50.

[source-1] 1.0 ^1.1 Kerem's Numbers - Left-Reverse Factorial Notation. Retrieved UTC 2023-08-10 05:27.

[source2-2] 2.0 ^2.1 Kerem's Numbers - Left-Reverse Factorial Notation. Retrieved UTC 2023-08-10 05:45.

[source3-3] 3.0 ^3.1 Kerem's Numbers - Left-Reverse Factorial Notation. Retrieved UTC 2023-08-10 15:50.

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