User blog:Stevenalexwcr1/My Array Notation

So, My array notation has parts ranging from basic to hyper-hyper-hyperdimensional arrays.

BAN, or Basic Array notation, Just the expression a|c|b or a ^^...^^b with c arrows! FGH limit: ω

2-entry array notation, does with 2 entries. Close equivalence with BEAF, but a rule applies called the switching rule, where the last 2 entries of BEAF are switched. FGH limit: ω^2

Linear arrays, entries are more than 2. FGH limit: ω^^3

Nested arrays (/), when used on 2 integers, it does this:

a|x / y|b = a|x, x...x, x|b with y x's. FGH limit: ε 0

I even have a|x // y|b =

a|x / x / x...x / x / x|b. Even the ///, which

the expression is a|x /// y|b,

does a|x // x...x // x // x|b for y x's

Ultradimensional (`) function, when used on 2 entries, does this:

a|x ` y|b = a|x //... // x|b with y /'s. FGH level: Γ 0

Hyper-nested arrays, has the format

a|x[k]y|b = a|x ``...`` y|b with k `s. FGH level: φ (1, 0, 0, 0)

Hyper-Hyper nested arrays, goes like

a|x k y|b = a|x[x[...[k]...]x]x|b with y pairs of ]['s. FGH level: r₀

Double commas, the first extension ever to reach the first uncountable ordinal(w₁ )

First order \, where it is done like

a|x \ y|b = a|x,,x...x,,x|b with y x's

I have another extension, the \\ where it is done as a|x \\ y|b = a|x \ x...x \ x|b

with y x's, and so forth. FGH level: ω₂

Now we have the Tilde-arrays, a new symbol is introduced, the tilde (~).

Where it is done as a|x ~ y|b =

a|x \\...\\ x|b with y \'s. FGH level: Φ1

Now we use Hedrondude's bracket-operator notation, where it's

a|x{k}y|b = a|x ... y|b with k ~'s

Again, we use Bowers' bracket-operator notation then we have a|x y|b,

where it's now a|x{x{...{k}...}x}x|b with y pairs of {}'s

I'm just going to insert this part here.

Now we have a|x#y|b =

a|x... [[x ...]]x|b with y []'s. FGH level = Small Veblen Ordinal

We use the ; to denote the following expression:

a|x;y|b = a|x x|b with x pairs of {}s. FGH level: Inaccessible cardinal (I)

Finally we have a|x * y|b = a|x;;...;;x|b

with x ;'s. FGH level: M (Mahlo cardinal)