On Wednesday, 2 November 2011 19:02:11 UTC+10, WM wrote: > On 2 Nov., 09:00, Virgil <vir...@ligriv.com> wrote: > > > If there is a bijection between |N and the set of digit positions in a > > string of digits then one has an actually infinite string > > There is a bijection between |N and the not so actually complete > string of all finite strings. > >
No there isn't.
> > > > (You see > > > this easily when considering the fact, that the complete tree cannot > > > be distinguished from a less complete tree by nodes). > > > > Actually not! There are 2^N paths in that tree, > > Not in that not so completely infinite tree of all finite paths.
Correct! One out of two is not so bad. Well done WM. I wonder if you realise why you are correct in this case though.
The actually correct number of paths in both cases is 0.
You see this easily when considering the fact that a tree with paths cannot be distinguished from a tree with only edges. No path contains more than all its edges. A path does not even have a complete realisation in edges or nodes since no matter the number of edges you add to a tree you will not yet have reached a path (you will only have more edges; and what more could you need?).
Your paths have to carry some kind of soul, invisible to the non believer, I suspect.
