User blog:Ynought/Tree like function

\(G_k\) is tree nr \(k\) and it has at most \(n+\text{the number of conections between nodes in the previous tree}\) in a set of trees (\(\{G_1,G_2,G_3...G_i\}\))

I will define \(i\) as the number of trees in a given set.

I will define \(j\in\mathbb{N}And \(b\(v_{a,b}\) is the \(a\)-th node (the order of the notes doesn't matter) in \(G_b\).Each node has to be assigned with the smallest number that didn't appear before and holds (i will call that number "\(x\)"):

\(V(v_{a,b})=\) the number assigned to \(v_{a,b}\)

\(f\) is some function that is primitive recursive(unless specified otherwise) and continuous.

\(f(V(v_{x,j}))\geqslant f(V(v_{x,j}))< f(V(v_{b,j}))<\omega\)

then \(T(n)=i+\text{the largest integer assigned to one of the nodes}\)

Let me know if this is actually well defined/works