User blog:Flitri/United Tree System

This is a backward (and possibly frontward) extension to the Fast-growing Hierarchy (FGH)

Each Unique Subscript can describe an operation, a notation, or even an hierarchy

--Regular Fast-growing Hierarchy (FGH) (also, R = Recursion)
F_R0(n) = n+1

F_Ra+1(n) = F^n_a(n) where f^n is Function Iteration

F_Ra(n) = F^n_a[n](n) if a is a limit ordinal

But: when a is only an integer

--Operators and linear BEAF arrays
F_aA(n,m,x...) = a+n+m+x... (S for subtraction)

F_aM(n,m,x...) = a*n*m*x*... (D for division)

F_aP(n,m,x...)= a^n^m^x^... (Power Towers, R for Roots)

F_aUm(n) = a{m}n = {a, n, m}

F_aUm(n; x, y, z ...) = {a, n, m, x, y, z...}

--Named but unquanitied (not given a numeric value, like Rayo's number) numbers
F_< (important) letters>(n) (if name has less than or equal to 3 letters write it in full; ex: Rayo -> Ryo and Sam -> Sam)

Ex: Fish Number 5 = F_FshNmbr(5), Rayo's Number = F_RyoNmbr(1)

--Factorials (unfinished)
F_aF(n)= a!n

F_aHF(n, m, x, y, z...) = a![n, m, x, y, z...] (when n=1, then aHF -> aF and (1, #) -> (1))

F_aMF(n) = a!!!! (when n=1, then aMF -> aF)

--Other Hierarchies
F_Ln(n) = Faster Growing Hierarchy

S_a(n) = Slow-growing Hierarchy

H_a(n) = Hardy Hierachy

--Extensible E system(s) (If a=10, then Ea -> E)
F_Ea(n, r1, r2, r3...) = E[a]n#r1#r2#r3...

F_Ea(nhb,chd,ehf...) = E[a]n##c##e##...

For g#^#*## = gAh

For i#^#### = iBj

For k#^#^(l) = kCl

For m#^#^^# = mDn