"Virgil" <firstname.lastname@example.org> wrote in message news:virgil-794EE9.18240822082013@BIGNEWS.USENETMONSTER.COM... > In article <email@example.com>, > "Julio Di Egidio" <firstname.lastname@example.org> wrote: > >> "Virgil" <email@example.com> wrote in message >> news:virgil-75DF2B.22094321082013@BIGNEWS.USENETMONSTER.COM... >> >> > Consider the binary tree in which every right child has a child and >> > every left child is a terminal node. >> > >> > Then there is in it for each member of |N a left terminal node having >> > that path length, and an infinite path of all right nodes to represent >> > the set |N itself, having one node at each length in |N. >> >> Just consider a unary tree. > > A unary tree will be a finite tree if and only if it has a terminal > node, unlike binary trees.
You asked for a tree with exactly one infinite path, not for a tree with terminal nodes. Indeed, as for "exact" representations of |N, what better than an infinite (and necessarily complete) unary tree, i.e. a simple sequence?