RIIOEL+DAN

***NOTE: A SERIOUS ERROR HAS BEEN MADE AND IT IS CURRENTLY BEING FIXED.***

## Starter Arrays

[a] = a a-ated to a ≈

f

ω

(
a
)

{\displaystyle f\_{\omega}(a)}

[a,2] = [[[...[[[a]]]...]]] a times ≈

f

ω
1

(
a
)

{\displaystyle f\_{\omega+1}(a)}

[a,3] = [[[...[[[a],2],2],2...],2],2],2] a times ≈

f

ω
2

(
a
)

{\displaystyle f\_{\omega+2}(a)}

etc.

[a,b,2] = [a,[a,[a,...[a,[a,[a,...]]]...]]] b times

[a,a,2] ≈

f

ω
a
1

(
a
)
<

f

ω
2
1

(
a
)

{\displaystyle f\_{\omega a+1}(a)<f\_{\omega 2+1}(a)}

etc.

[a,b,1,2] = [a,a,[a,a,[a,a,[...]]]...]]]

[a,a,1,2] ≈

f

ω
3

(
a
)

{\displaystyle f\_{\omega3}(a)}

etc.

## Large Linear Arrays

[a,b(1)2] = [a,a,a...,a,a,a] with b copies of a

[a,a(1)2] ≈

f

ω
ω

(
a
)

{\displaystyle f\_{\omega^\omega}(a)}

⌣
¨

→

^

^

¯

~

~

˘

ˇ

`

´

¨

˙

{\displaystyle \dot{\ddot{\acute{\grave{\check{\breve{\tilde{\widetilde{\bar{\hat{\widehat{\vec{\ddot{\smile}}}}}}}}}}}}}}

A weird thingy I made that has nothing to do with this.

Continue after [a,b(1)2].

### Higher Exponential Arrays

[a,b(1)1(1)2] = [a,a(1)1,1,1...,1,1,2] b times

[a,a(1)1(1)2] ≈

f

ω

ω
2

(
a
)

{\displaystyle f\_{\omega^{\omega2}}(a)}

etc.

## Dimensional Arrays

~~[a,b(2)2] = [a,a(1)1(1)1(1)1...1(1)1(1)1(1)2] b times but then do whatever you need to do to make the approximation below true:~~

~~[a,a(b)2] ≈

f

b
1

ω

(
a
)

{\displaystyle f\_{^{b+1}\omega}(a)}~~

~~continue etc.~~

~~[a,a(a)2] ≈

f

ε
0

(
a
)

{\displaystyle f\_{\varepsilon\_0}(a)}~~

UPDATE:

[a,b(1)(1)2] = [a,a(1)1(1)1(1)1...1(1)1(1)1(1)2] b times

etc.

[a,b(2)2] = [a,a(1)(1)(1)...(1)(1)(1)2] b times

[a,a(2)2] ≈

f

ω

ω
ω

(
a
)

{\displaystyle f\_{\omega^{\omega^\omega}}(a)}

etc.

[a,a(a)2] ≈

f

ε
0

(
a
)

{\displaystyle f\_{\varepsilon\_0}(a)}

### Nestimensional Arrays

[a,b(1,2)2] is the nesting of [a,a(a)2] b times.

[a,a(1,2)2] ≈

f

ε
0

1

(
a
)

{\displaystyle f\_{\varepsilon\_0+1}(a)}

etc.

[a,a(1(1)2)2] ≈

f

ε
0

ω
2

(
a
)

{\displaystyle f\_{\varepsilon\_0+\omega^2}(a)}

## Tetrational Arrays

[a,b(1[1]2)2] = [a,a(1(1(1...(1(1(1)1)1)1...)1)1)2)] b times

[a,a(1[1]2)2] ≈

f

ε

ω

(
a
)

{\displaystyle f\_{\varepsilon\_{\omega}}(a)}

etc.

## Pentational Arrays and Beyond

[a,b[3];(1[1]2)2] = [a,a(1[1[1...[1[1[1]1]1]1...]1]1]1)2] b times

[a,a[3];(1[1]2)2] ≈

f

Γ

ω

(
a
)

{\displaystyle f\_{\Gamma\_{\omega}}(a)}

You can continue with [4];(1[1]2), [5];(1[1]2), etc.

[a,a[4];(1[1]2)2] ≈

f

Ϝ

ω

(
a
)

{\displaystyle f\_{\Digamma\_{\omega}}(a)}

(

Ϝ

α

=
φ
(
2
,
0
,
α
)

{\displaystyle \Digamma\_{\alpha} = \varphi(2,0,\alpha)}

)

### Nesting

Start to form arrays inside of [];.

[a,b[1/2]2] = The nesting of [[a];(1[1]2)];(1[1]2)2] b times

[a,a[1/2]2] ≈

f

ψ
0

(

Ω

ω

)

(
a
)

{\displaystyle f\_{\psi\_0(\Omega\_{\omega})}(a)}

(I think, the rest is currently incorrect, so it's hard to tell)

[a,b[2/2]2] = [a,a[1/2]1[1/2]1[1/2]...1[1/2]1[1/2]1[1/2]2]

etc.

When you get to something like [a,b[(1/2)/2]2], it would be [a,b[1/3]2].

etc.

#### Higher Nesting

[a,b[1//2]2] = [a,a[1/1/1/...1/1/1/2]2] b times

[a,a[1//2]2] ≈

f

φ
(
1
,
0
,
0
,
0
,
ω
)

(
a
)

{\displaystyle f\_{\varphi(1,0,0,0,\omega)}(a)}

etc.

[a,b[1/(1)2]2] = [a,a[1///...///2]2] b times

[a,a[1/(1)2]2] ≈

f

ϑ
(

Ω

ω

)

(
a
)

{\displaystyle f\_{\vartheta(\Omega^{\omega})}(a)}

etc.

## M O R E

Then, start nesting [a,a[1/[1/2]2]2] b times to get [a,b[1\2]2].

[a,a[1\2]2] ≈

f

ϑ
(

Ω

Ω

ω

)

(
a
)

{\displaystyle f\_{\vartheta(\Omega^{\Omega^{\omega}})}(a)}

Continue with \.

Nest \ to get |.

Keep doing that to get [a,b[1♦2]2].

[a,a[1♦2]2] ≈

f

ϑ
(

Ω
2

)

(
a
)

{\displaystyle f\_{\vartheta(\Omega\_2)}(a)}

Nest ♦ like you did with /, \, and |.

Nest that to get •.

Keep doing that to get ♣.

[a,a[1♣2]2] ≈

f

ϑ
(

Ω

ω

)

(
a
)

{\displaystyle f\_{\vartheta(\Omega\_{\omega})}(a)}

Nest ♣ to get ♠.

[a,a[1♠2]2] ≈

f

ϑ
(

Ω

Ω

ω

)

(
a
)

{\displaystyle f\_{\vartheta(\Omega\_{\Omega\_{\omega}})}(a)}

Keep doing that to get ◘.

[a,a[1◘2]2] ≈

f

ϑ
(
≀
(
Ω
,
Ω
,
0
)
)

(
a
)

{\displaystyle f\_{\vartheta(\wr(\Omega,\Omega,0))}(a)}

(see Infinity Fusing Notation)

## I N S A N I T Y

### The ○'s

Nest ◘ to get ○.

[a,a[1○2]2] ≈

f

ϑ
(
≀
(
Ω
,
Ω
,
1
)
)

(
a
)

{\displaystyle f\_{\vartheta(\wr(\Omega,\Omega,1))}(a)}

### The ◙'s

Nest ○ to get ◙.

[a,a[1◙2]2] ≈

f

ϑ
(
≀
(
Ω
,
Ω
,
2
)
)

(
a
)

{\displaystyle f\_{\vartheta(\wr(\Omega,\Omega,2))}(a)}

### The ♪'s

Keep doing that to get ♪

[a,a[1♪2]2] ≈

f

ϑ
(
≀
(
Ω
,
Ω
,
ω
)
)

(
a
)

{\displaystyle f\_{\vartheta(\wr(\Omega,\Omega,\omega))}(a)}

## OMNI

Use legions like BEAF.

Alternate notation that will get big.

[a,b[1'2]2] is like {a,b/2}.

[a,b[1"2]2] is like {a,b//2}.

WIP!

## Numbers

Sogol = [100]

Gozol = [10,100]

Dozol = [10,100,2]

Trozol = [10,100,3]

Tetrozol = [10,100,4]

etc.

Unduypozol = [10,100,1,2]

Duduypozol = [10,100,2,2]

Triduypozol = [10,100,3,2]

etc.

Duwzol = [10,10,100,2]

Untriypozol = [10,100,1,3]

All extensions apply.

Triwzol = [10,10,100,3]

Untetraypozol = [10,100,1,4]

Tetrawzol = [10,10,100,4]

etc.

Trezol = [10,10,10,100]

Dueide Trezol = [10,10,10,100,2]

Tride Trezol = [10,10,10,100,3]

Tetred Trezol = [10,10,10,100,4]

etc.

Tetrezol = [10,10,10,10,100]

Pentezol = [10,10,10,10,10,100]

Hexezol = [10,10,10,10,10,10,100]

Gonlinol = [10,100(1)2]

All extensions apply.

Gonlinoltri = [10,100(1)3]

Gonlinoltet - [10,100(1)4]

etc.

Gonlinolunduyp = [10,100(1)1,2]

etc.

Gozol-ata-Gonlinol = [10,10(1)10,100]

etc.

Donlinol = [10,100(1)1(1)2]

etc.

Tronlinol = [10,100(1)1(1)1(1)2]

Tetronlinol = [10,100(1)1(1)1(1)1(1)2]

etc.

Gonplanol = [10,100(2)2]

etc.

Goncubol = [10,100(3)2]

Gontessol = [10,100(4)2]

Gonpentol = [10,100(5)2]

Golocacash = [10,10(100)2]

Unduyp Golocacash = [10,100(1,2)2]

etc.

Dolocacash = [10,100(1(1)2)2]

Trolocacash = [10,100(1(1(1)2)2)2]

etc.

Noinkuduwulus = [10,100(1[1]2)2]

etc.

Noinkuduwugrid = [10,100(1[2]2)2]

Noinkuduwuspace = [10,100(1[3]2)2]

Noinuduwutime = [10,100(1[4]2)2]

etc.

Golodacash = [10,100(1[100]2)2]

Golocanoinkudu = [10,100(1[1(1)2]2)2]

Dolocanoinkudu = [10,100(1[1(1(1)2)2]2)2]

etc.

Dolodacash = [10,100(1[1[1]2]2)2]

etc.

Noinkutriwulus = [10,100[3];(1[1]2)2]

etc.

Noinkutetrawulus = [10,100[4];(1[1]2)2]

Noinkupentawulus = [10,100[5];(1[1]2)2]

etc.

Noinkareew = [10,10[100];(1[1]2)2]

Noinkunduypulus = [10,100[1,2];(1[1]2)2]

etc.

Duatakoinun = [10,100[1(1)2];(1[1]2)2]

Duatakoindu = [10,100[1[1]2];(1[1]2)2]

Duatakointri = [10,100[[3];(1[1]2)];(1[1]2)

etc.

etc.

Slashagol = [10,100[1/2]2]

WIP‼

FREE-TO-EXTEND‼

***EXTREMELY INSANELY WIP‼‼‼***