In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 16 Jan., 08:44, Virgil <vir...@ligriv.com> wrote: > > In article > > <0d0383dd-82ff-420c-a045-461df2411...@u19g2000yqj.googlegroups.com>, > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 15 Jan., 22:56, Virgil <vir...@ligriv.com> wrote: > > > > > > Why can my string not differ from the nth finite string in your listing > > > > of finite strings in that string's nth place, if that string has one, > > > > and by having anything in my strng's nth place if your nth string is not > > > > n places long? > > > > I see no reason why my string cannot differ from each string in your > > > > whole list of strings according to such a rule. > > > > > Your string can and will differ from the nth string. But there will > > > always an identical string be in the list > > > > Identical to what? > > Identical to every initial segment of the anti-diagonal.
If that alleged "identical string" were in some position n in the list then it will differ from any anti-diagonal at its own position n.
So there is nowhere in the list that t can occur without differing from an antidiagoal.
Thus WM is WONG! AGAIN!! As USUAL!!!
> > > Every > > > finite string means that there is no chance to construct something > > > deviating from all. > > > > That only hold in WMytheology, if anywhere. > > Why should a list of all finite strings be impossible?
That is not what I objected to.
What I object to is your claim that some finite string will be the same as an infinite string. > > > > Thus WM's infinite list of finite sequences argument is just special > > case of Cantor's infinite list of infinite sequences arguments, and thus > > fails. > > Of course any Cantor-list that contains all finite strings fails to > produce a different finite string.
But if it produces an infinite string, that too will differ from all finite strings.
WM is confused. No one is claiming that the set of finite strings is uncountable, so WM's listings of finite strings is irrelevant.
> The Binary Tree is an example.
What WM claims for trees only holds for trees in which all paths are finite, but this excludes the Complete Infinite Binary Tree.
The Complete Infinite Binary Tree is a counter-example to WM's idiotic claims.
> After all finite initial segmenst of paths there is no chance to > differ by nodes.
Any two different paths in any sort of binary tree "differ by nodes" so that there are no trees finite or otherwise, satisfying WM's requirements.
> And the handwaving claim to "differ in the infinite" > can be rejected by stating that in mathematics there is no chance to > differ in the infinite.
That not being what is claimed for a true Complete Infinite Binary Tree, it is an irrelevancy.
What is claimed, and what is true, is that any two distinct paths in a CIBT differ at infinitely many finite levels, i.e., will have only a finite initial sequence of nodes in common, and not have any other of their infinitely many nodes in common.
Perhaps if WM had any real comprehension of what a Complete Infinite Binary Tree is like he would not make so many mistakes about them. --