On 25 Jan., 09:26, Virgil <vir...@ligriv.com> wrote:
> > How do you express actual infinity by means of nodes or levels? > > Try it. > > Write a sequence like xxxxxxxxxx... and do never stop. > > It is the knowledge that it never stops that makes it NOT FINITE.
Yes you need some external "knowledge" or better say trust in matheology.
> It is also the knowledge that no finite initial segment of natural > numbers (fison) surjects onto it that makes it infinite.
That is correct in every case. The reason could be that N does not exist as something completed. > > > Tell me when you have expressed an infinite sequence. > > Tell me when you can surject a fison onto it.
I am fairly sure that I can surject a FISON on that sequence that you may have produced today, even if you have started very early. > > > > > > We can use the same set of nodes to make two collections of > > > sets of nodes. One collection contains all sets of nodes, X, with > > > the property that there is a node in X with a level greater or > > > equal to that of any other node in X. > > > The other collection contains all sets of nodes, Y, with the property > > > that there is no node in Y with a level greater or equal to that of > > > any other node Y. > > > No. You cannot express the latter by nodes and levels. If you don't > > believe me, try it. > > We have already done so to our own satisfaction, by showing that no > fison surjects onto any a path ( as a sequnce of nodes) in a real > Complete Infinite Binary Tree
So the complete infinite paths must extend beyond every finit path in the tree? And if the tree contains only all finite paths, then we have something like the bed of Procrustes. What shall we do? Cut the tails that are too long? I would be glad to do so, but I have never seen any. Perhaps it is only an apparition of matheology if you see such tails?