In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 2 Apr., 02:01, Virgil <vir...@ligriv.com> wrote: > > In article > > <1dd2037c-407c-49f6-afc6-e00c1d853...@w21g2000vbp.googlegroups.com>, > > > > > > > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 1 Apr., 22:44, Virgil <vir...@ligriv.com> wrote: > > > > > > > You do not believe that a sequence or list of all rational numbers can > > > > > be constructed? > > > > > > One can "enumerate" the set of all rationals by formula, as has been > > > > quite often done, but not by physically listing all of them. > > > > > A formula giving every entry is enough. > > > > > > Note that one cannot ennumerate by listing even sufficiently large > > > > finite sets, so being listable other than by formula is not a relevant > > > > criterion. > > > > > Constructing a list by a formula is enough to prove what I said. > > > > And enough to disprove what WM has said as well. > > Then try it. > What did I say?
Among other things, WM has said that in a COMPLETE INFINITE BINARY TREE there are paths of finite length, but as paths are, by definition, only MAXIMAL sequences of parent-child linked nodes and EVERY node has child nodes, there cannot be any such sequence of parent-child linked nodes which is both finite and maximal.
What WM miscalls paths are merely FISONs (finite initial sequences of nodes), no one of which fails to be a PROPER subset of some other FISON, and thus cannot be maximal and thus cannot be a path. --