User blog:Antares.I.G.Harrison/The Graham Array Notation Reloaded

This is a rework of my GAN project

(# means an array, or the rest of an array)

Any 0's may be Cropped Off

Any 1's will become : [a,#,1,#] = [a,#]

So any 1's disapper with anything behind it

[a] = a

[a,b] = ab

[a,b,c] = a↑↑...↑↑b (c ↑'s)

[a,b,c,d] = a{a...a{a{c}b}b...b}b (d {}'c) (BEAF)

For [#] with 5 or more entries, we define a BEAF-like function.

The Last Entry : "Leader"

The Second-to-last Entry : "Helper"

5+ Entry arrays are defined as

[a,b,c,d,e] = [a,b,c,[a,b,c,d,e-1]]

So the "Leader" Disappears and the "Helper" is changed into the array itself, only with the "Leader" decreasing by 1]

So let's go on

[a,b,c,d,e,f] = [a,b,c,d,[a,b,c,d,e,f-1]]

[a,b,c,d,e,f,g] = [a,b,c,d,e,[a,b,c,d,e,f,g-1]]

[a,b,c,d,e,f,g,h] = [a,b,c,d,e,f,[a,b,c,d,e,f,g,h-1]]

A new function :

[a^b] = [a,a,a,.....,a,a,a] with b a's

Dimensional arrays

Dimensional arrays are arrays that need 2 or more dimensions to represent.

An examples is [2(3)2], which is a cube of [2^2] = [2,2]'s that has a side lenght of 2.

2-dimensional arrays would look something like this :

|10^10| |10^10| |10^10|

They are all connected with ^'s, so 10^10]^[10^10]^[10^10

Please don't point out ill-definitions. Please imagine BEAF's arrays. This is a WIP project.

[a^^b] = [a^a^....^a^a] with b a's

[a^^^b] = [a^^a^^a...a^^a^^a] with b a's

And so on (No problems here)

[a<^>b] = [a^^^...^^^a] with b ^'s

[a<<^>>b] = [a<^>a<^>a...a<^>a<^>a] with b a's

[a<<<^>>>b] = [a<<^>>a<<^>>.....<<^>>a<<^>>a] with b a's

[a/b] = [a<<...<<^>>...>>a] with b <>'s

[a//b] = [a/a/a...a/a] with b a's

[a///b] = [a//a//a...a//a] with b a's

[a\b] = a(b)a(b)...(b)a]/[a(b)a(b)...(b)a]/[a(b)a(b)...(b)a]/........../[a(b)a(b)...(b)a]/[a(b)a(b)...(b)a

There are a a's in [a(b)a(b)...(b)a] and b [a(b)a(b)...(b)a]'s overall

[a\\b] = [a\a\a...\a] (b a's)

[A,a] = [a\\...\\a] (a \'s)

[A,A,a] = [A,[A,a]]

[A2,a] = [A,A,A,...,A,a] with a A's

[A3,a] = [A2,A2,A2,.....,A2,a] with b A2's

[An,a] = [An-1,An-1,An-1,...,An-1,a] with a An-1's

Wew! :)