On 29 Mrz., 19:40, Virgil <vir...@ligriv.com> wrote: > In article > <ce3c22f2-9116-4621-b3b4-e722fe51a...@a14g2000vbm.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 26 Mrz., 22:47, Virgil <vir...@ligriv.com> wrote: > > > > But a tree that contains paths for all binary rationals will contain a > > > path for all limits of a sequences of binary rationals. > > > Does a sequence always contain its limit? > > Depends on the sequence, of course. but a sequence of paths in a > Complete Infinite Binary Tree in which the nth path must share at least > n nodes with each of its successors will always converge, though not > neccessarily to a binary rational.
A sequence of numbers may converge, but not necessarily to a limit that is a term of the sequence. A sequence of paths may converge, but not necessarily to a limit that is a term of the sequence. If you believe in a difference between numbers and paths, you should be able to substantiate that belief. But you cannot reason with mathematical arguments. Again you have to believe in matheology as the "reason" of this difference.
In mathematics more precision is required.
> > > > In a COMPLETE INFINITE BINARY TREE, all paths are actually infinite, so > the issue does not arise.. > --
This is again a simple statement of countermathematical belief and as such without value in mathematics.