RIIOEL+DAN

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

Starter Arrays
[a] = a a-ated to a ≈ $$f_{\omega}(a)$$

[a,2] = [...[[[a]...]]] a times ≈ $$f_{\omega+1}(a)$$

[a,3] = [[[...[[[a],2],2],2...],2],2],2] a times ≈ $$f_{\omega+2}(a)$$

etc.

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

[a,a,2] ≈ $$f_{\omega a+1}(a)<f_{\omega 2+1}(a)$$

etc.

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

[a,a,1,2] ≈ $$f_{\omega3}(a)$$

etc.

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

[a,a(1)2] ≈ $$f_{\omega^\omega}(a)$$

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

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] ≈ $$f_{\omega^{\omega2}}(a)$$

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] ≈ $$f_{^{b+1}\omega}(a)$$

continue etc.

[a,a(a)2] ≈ $$f_{\varepsilon_0}(a)$$

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] ≈ $$f_{\omega^{\omega^\omega}}(a)$$

etc.

[a,a(a)2] ≈ $$f_{\varepsilon_0}(a)$$

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

[a,a(1,2)2] ≈ $$f_{\varepsilon_0+1}(a)$$

etc.

[a,a(1(1)2)2] ≈ $$f_{\varepsilon_0+\omega^2}(a)$$

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] ≈ $$f_{\varepsilon_{\omega}}(a)$$

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] ≈ $$f_{\Gamma_{\omega}}(a)$$

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

[a,a[4];(1[1]2)2] ≈ $$f_{\Digamma_{\omega}}(a)$$($$\Digamma_{\alpha} = \varphi(2,0,\alpha)$$)

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] ≈ $$f_{\psi_0(\Omega_{\omega})}(a)$$(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] ≈ $$f_{\varphi(1,0,0,0,\omega)}(a)$$

etc.

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

[a,a[1/(1)2]2] ≈ $$f_{\vartheta(\Omega^{\omega})}(a)$$

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] ≈ $$f_{\vartheta(\Omega^{\Omega^{\omega}})}(a)$$

Continue with \.

Nest \ to get |.

Keep doing that to get [a,b[1♦2]2].

[a,a[1♦2]2] ≈ $$f_{\vartheta(\Omega_2)}(a)$$

Nest ♦ like you did with /, \, and |.

Nest that to get •.

Keep doing that to get ♣.

[a,a[1♣2]2] ≈ $$f_{\vartheta(\Omega_{\omega})}(a)$$

Nest ♣ to get ♠.

[a,a[1♠2]2] ≈ $$f_{\vartheta(\Omega_{\Omega_{\omega}})}(a)$$

Keep doing that to get ◘.

[a,a[1◘2]2] ≈ $$f_{\vartheta(\wr(\Omega,\Omega,0))}(a)$$(see Infinity Fusing Notation)

The ○'s
Nest ◘ to get ○.

[a,a[1○2]2] ≈ $$f_{\vartheta(\wr(\Omega,\Omega,1))}(a)$$

The ◙'s
Nest ○ to get ◙.

[a,a[1◙2]2] ≈ $$f_{\vartheta(\wr(\Omega,\Omega,2))}(a)$$

The ♪'s
Keep doing that to get ♪

[a,a[1♪2]2] ≈ $$f_{\vartheta(\wr(\Omega,\Omega,\omega))}(a)$$

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]

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