Virgil
Posts:
8,833
Registered:
1/6/11


Re: Matheology � 233
Posted:
Apr 2, 2013 5:56 PM


In article <7ab07dbcc9b148af8e59d91cf271b228@c15g2000vbl.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 2 Apr., 02:01, Virgil <vir...@ligriv.com> wrote: > > In article > > <1dd2037c407c49f6afc6e00c1d853...@w21g2000vbp.googlegroups.com>, > > > > > > > > > > > > WM <mueck...@rz.fhaugsburg.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 parentchild linked nodes and EVERY node has child nodes, there cannot be any such sequence of parentchild 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. 

