Description

The Terribly-Big Array Notation (TBAN) is an array notation that gradually grows.

Base rules

Legend:
# = arbitrary length array of any number
$ = arbitrary length array of ones

[#]_1 = [#]
[1,#]_x = 1 (when x ≥ 3)
[#]_x,$ = [#]_x

Definition

We use square brackets like this [a,b] and we define this as [a,b] = a+b but you can also [a,b,c] = a+b+c, then we have [a,b,c,d,e,f...] = sum(a,b,c,d,e,f...)

This is where we use subscripts because we now do [a,b]_2 = [a,a,a,a,a,a,a,a,a...] (b times) = a*b
and then [a,b,c]_2 = a*b*c
and [a,b]_3 = a^b,  [a,b,c]_3 = a^(b^c)
so on, [a,b]_4 = a^^b, [a,b]_5 = a^^^b...  (hyperoperator function)
Now we do something, we now use commas like [a,b]_x,2 = [a,b]_[a,b]_x
and then [a,b]_x,3 = [a,b]_[a,b]_[a,b]_x.
[a,b]_x,y = [a,b]_[a,b]_[a,b]_...[a,b]_x.

Now lets do something,
we now use an alternative notation to represent these subscripts, we use slashes "/"
[a,b/2] = [a,b]_2 = a*b
[a,b/c] = [a,b]_c = H_c(a,b)
[a,b/1,2] = [a,b/[a,b/1]] = H_(a+b)(a,b)
and for that, we add a third comma
[a,b/1,2,2] = [a,b/[a,b/1,2],2]
and a fourth
[a,b/1,2,2,2] = [a,b/[a,b/1,2,2],2,2]
and so on
[a,b/1,2,2,2,2] = [a,b/[a,b/1,2,2,2],2,2,2]
[a,b/c,d...(x ammount)...d] = [a,b/[a,b/c,d...(x-1 ammount)...d],d...(x-1 ammount)...d]

Now to represent this thing above, we do THIS
[a,b/c,,d,e] = [a,b/c,d...(e ammount)...d]
as well as
[a,b/c,,d,e,f] = [a,b/c,d...([e,f] ammount)...d]
[a,b/c,,d,e,f,g] = [a,b/c,d...([e,f/g] ammount)...d]
[a,b/x_0,,x_1,x_2,x_3...x_n] = [a,b/x_0,x_1...([x_2,x_3/x_4,x_5...x_n] ammount)...x_1]
and wow, it may give us large numbers. and thats it, for now. This is just one part of a larger system (The Terribly-Big System) that is still in development