## FANDOM

10,837 Pages

Here is my extension.

## Up to gamma(0)

a&<2>[A](x) = a&<1>[&<1>[&<1>[...[&<1>[&<1>[A]]]...]]](x) with x levels

a&<n>[A](x) = a&<n-1>[&<n-1>[&<n-1>[...[&<n-1>[&<n-1>[A]]]...]]](x) with x levels

a&<A>[A](x) = a&<x>[A](x)

etc.

### FGH

a&<2>[A](x) = z(0)

a&<3>[A](x) = eta(0)

a&<A>[A](x) = phi(w,0)

a&<&[A]>[A](x) = phi(w^w,0)

a&<&<1>[A]>[A](x) = phi(e(0),0)

a&<&<A>[A]>[A](x) = phi(phi(w,0),0)

So the limit is gamma(0)

## Up to SVO

a&<1><2>[A](x) (cookiefonster suggested changing this to a&<1,2>[A](x)) = a&<&<&<...<&<&<&<A>[A]>[A]>[A]>...>[A]>[A]>[A](x) with x levels

a&<2><2>[A](x) = a&<1><2>[&<1><2>[&<1><2>[...[&<1><2>[&<1><2>[&<1><2>[A]]]]...]]](x) with x levels

a&<1><3>[A](x) = a&<&<&<...<&<&<&<A><2>[A]><2>[A]><2>[A]>...><2>[A]><2>[A]><2>[A](x) with x levels

a&<1><1><2>[A](x) = a&<1><&<1><&<1><...<1><&<1><&<1><&<1><A>[A]>[A]>[A]>...>[A]>[A]>[A](x) with x levels

etc.

### FGH

a&<1><2>[A](x) = gamma(0)

a&<2><2>[A](x) = phi(1,1,0)

a&<1><3>[A](x) = phi(2,0,0)

a&<1><1><2>[A](x) = phi(1,0,0,0) = theta(W^2) = Ackermann Ordinal

etc.

So limit is theta(W^w) (SVO)

## Up to ??? (Linear Array Angle Brackets)

a&<1>,<2>[A](x) = a&<1><1><1>...<1><1><2>[A](x) with x angle brackets

a&<2>,<2>[A](x) = a&<1>,<2>[&<1>,<2>[&<1>,<2>[...[&<1>,<2>[&<1>,<2>[&<1>,<2>[A]]]]...]]](x) with x levels

a&<1><2>,<2>[A](x) = a&<&<&<...<&<&<&<A>,<2>[A]>,<2>[A]>,<2>[A]>,<2>...>,<2>[A]>,<2>[A]>,<2>[A](x) with x levels

a&<1>,<3>[A](x) = a&<1><1><1>...<1><1><2>,<2>[A](x) with x angle brackets

a&<1>,<1><2>[A](x) = a&<1>,<&<1>,<&<1>,<...<1><&<1>,<&<1>,<&<1>,<A>[A]>[A]>[A]>...>[A]>[A]>[A](x) with x levels

a&<1>,<1>,<2>[A](x) = a&<1>,<1><1><1>...<1><1><2>[A](x) with x angle brackets

etc.

### FGH

Support analysis if you want.

## Up to ??? (Dimensional Array Angle Brackets)

a&<1>(2)<2>[A](x) = a&<1>,<1>,<1>,...,<1>,<1>,<2>[A](x) with x angle brackets

a&<1><2>(2)<2>[A](x) = a&<&<&<&<...<&<&<&<1>(2)<2>[A]>(2)<2>[A]>(2)<2>[A]>...>(2)<2>[A]>(2)<2>[A]>(2)<2>[A]>(2)<2>[A](x) with x levels

a&<1>,<2>(2)<2>[A](x) = a&<1><1><1>...<1><1><2>(2)<2>[A](x) with x angle brackets

a&<1>(2)<3>[A](x) = a&<1>,<1>,<1>,...,<1>,<1>,<2>(2)<2>[A](x) with x angle brackets

a&<1>(2)<1>(2)<2>[A](x) = a&<1>{A]<1>,<1>,<1>,...,<1>,<1>,<2>(x) with x angle brackets

a&<1>(3)<2>[A](x) = a&<1>(2)<1>(2)<1>(2)...(2)<1>(2)<1>(2)<2>[A](x) with x angle brackets

etc.

### FGH

Support analysis if you want.

## Up to ??? (Nested Dimensional Array Angle Brackets)

-- UNDER CONSTRUCTION --

NOTE: Closing this project because i don't want to put my overload of array operators here.