Right-Reverse Factorial Notation

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Right-Reverse Factorial Notation is a notation coined by Googology Wiki user AblanGG. Unfortunately, versions of the notation are ill-defined by the reason explained in #Issues section. Even if there will be new versions for which this article does not clarify issues, this does not mean those versions are well-defined because this article is not a

Definition

Original version

Here is the copy of the definition in the source:

\(n,m \in \mathbb{R}, z \in \mathbb{N}\)

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

Second version

Here is the copy of the definition in the updated source:

\(n,m,z \in \mathbb{N}\)

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

Third version

Here is the copy of the definition in the updated source:

\(n,m,z \in \mathbb{N+}\)

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

Issues

Similar to Kerem's Number#Issues, the definition is just given by a rough descpription with seriusly ambiguous repetition of ellipses. For example, the evaluation of \(\sqrt{2}!\), which is a valid expression in this notation because \(\sqrt{2} \in \mathbb{R}\), is ambiguously descrived as \(\sqrt{2} \times (\sqrt{2} - 1) \times \cdots 2 \times 1\).

• The creator later solved the problem on \(\sqrt{2}\), by making \(n,m\) and \(z\) can only be positive integers. The ellipses still appear, though.

We note that the issue above is just an example, and hence solving it does not mean that the notation bacomes well-defined. For example, since the definition is just given by incomplete partial specialisation, there is no rigorous description applicable to 13¡¡.