User blog:Ubersketch/Hypernomial Hierarchy v3

\(0(n)=0\)

\(S(n)=n+1\)

\(f(a)[n]=f(a[n])\) where \(a\) is a limit erdinal.

\(f(n)\circ g(n)=g(f(n))

\(f(n)@g(n)=\underbrace{f(n)\circ f(n)\circ f(n)...}_{g(n)\textrm{ amount of} f(n)}\)

\(0(n)\in h\)

\(S(n)\in h\)

\(a[n]\in h\) where \(a\in H\)

\(f(n)\circ g(n)\in h\) where \(f(n)\) and \(g(n)\in h\)

\(f(n)@g(n)\in h\) where \(f(n)\) and \(g(n)\in h\)

\(0\in H\)

\(w\in H\)

\(f(n)\in H\) where \(f(n)\in h\) and \(n\in H\)

\(H\) are the hypernomials.