Virgil
Posts:
9,012
Registered:
1/6/11


Re: On the infinite binary Tree
Posted:
Dec 13, 2012 6:00 PM


In article <3b6bcd8386754a0a80222e0e0386e7ca@n5g2000vbk.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 13 Dez., 20:57, Zuhair <zaljo...@gmail.com> wrote: > > > > Are you are too dishonest, to confess your error? Or do you really not > > > understand, that your pieces of paths are irrelevant? > > > > They are indeed relevant. > > For what? > > > We don't need the zero before the decimal > > point at all, all what we need is the string of digits AFTER the > > decimal, > > i.e., after the 0. So the string begins with 0 as I said and not with > 1 as you tried to show. > > > Your argument is simply the following: > > > > All reals are definable by parameter free finite formulas. > > > > Since we have countably many of those formulas. > > > > Then we have countably many reals. > > > > This argument is FALSE, simply because not all reals are definable by > > parameter free finite formulas. > > Wrong. My argument is simply that you cannot find out by nodes which > paths I use to construct the complete Binary Tree. Therefore you > cannot defined by nodes which paths are missing.
That one cannot get there by one road does not prove one cannot get there by another, however much WM would like it to be so.
To prove that a set is missing some paths, it is enough to prove that set is simply not big enough, without worrying about which elements are missing.
And it has frequently been shown that set of all possible paths is not countable whereas WM's set of paths, by his own claims, is countable. 

