RMI: Notations (Side)

I will use a substitute function but it will represent "a_{§}"

§(a) = ω + a

<§+b>(a) = ω + <§+(b-1)>(a)

<§*2>(a) = ω + <§+§(a)>(a)

<§*b>(a) = ω + <§+<§*(b-1)>(a)>(a)

ect

base definitions:

| = 1

|| = 2

||| = 3

|||| = 4

! = 5

|! = 6

||! = 7

|||! = 8

||||! = 9

ect

notation:

|[|] = 10
|[||] = 100
|[|||] = 1000
|[x] = 10^x
||[x] = 10^(10^x)
y[x] = 10^((y-1)[x])
|[[x]] = (|[|])[(x[x])]
y[[x]] = (|[|])[((y-1)[[x]])]
|[[[x]]] = (|[|])[(x[[x]])]
y[[[x]]]  = (|[|])[((y-1)[[[x]]])]
ect

x< = x-1
x<[y] = x-(|[y])
_ = ω

{]0[} = 100
{]x[} = 10^{]x-1[}
{]x,0[} = {]x[}
{]x,y[} = {]{]x,y-1}[}[}
{]x,y,0[} = {]x,y[}
{]x,y,z[} = {]{]x,y,z-1[},{]x,y,z-1[}[}
{]x,y,z,α[} = {]{]x,y,z,α-1[},{]x,y,z,α-1[},{]x,y,z,α-1[}[}
{]a...ψ,ω[} = {]{]a...ψ,ω-1[}...{]a...ψ,ω-1[}[}

Side Inputs

{1]x[} = {]x,x,x,x,x,x,x,x...[} (x copies of x) = {1]x,y[}
{1]x,y[} ={1]{1]x,y-1[}[}
{1]x,y,z[} = {1]{1]x,y,z-1[},{1]x,y,z-1[}[}
ect

{Λ]x[} = {Λ-1]x,x,x,x,x,x,x,x...[} (x copies of x)
{Λ]x,y[} ={Λ]{Λ]x,y-1[}[}
{Λ]x,y,z[} ={Λ]{Λ]x,y,z-1[},{Λ]x,y,z-1[}[}
ect

the dumb notation

Σ = 1
Σ+1 = 11
Σ+2 = 12
ΣΣ+1 = 21
(Σ*2)+1 = 111
Σ. + 5 = 1.5

f(...) =: H[#]{#}H[#+1], # (# represents the entry number, H represents the list of entries) where f(2,2,2) = 2^2^^2

Extra input areas (examples)

f(?)(...) = f(H){#}f(?)
f(2,2,2)(2,2) = (2^2)^(2^2^^2)

f(...)(n) = f(f(H),f(H),f(H)...{n}.)(n-1)

i(o,t) creates an imaginary number that fullfills the statement(/s) t using o to solve for, this is simple