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


Re: WM misexplains what he means by a Binary Tree
Posted:
Feb 7, 2014 2:54 PM


In article <0ba1cb37bc0949baace2a97684ffe3ec@googlegroups.com>, WM <wolfgang.mueckenheim@hsaugsburg.de> wrote: > Am Donnerstag, 6. Februar 2014 22:46:41 UTC+1 schrieb Virgil: > > In article <a37eee53513b42999c3036ec271eaec1@googlegroups.com>,
> > > > The finitely defined real number r = Sum_(n in N) 1/2^(n!), in base > > > > 2, > > > > is not anywhere in WM's "rationalscomplete list"
> > > No it is not since it cannot be represented by digits.
But it is finitely defined real number anyway!
> > It IS representable by digits in base 2 by having a 1 in each n! place > > and 0's elsewhere. > The set of these digits is in the set of all finite approximations of r. Is r > in that set too?
The set of those digits is in {0,1} but r is not in {0,1} either!.
> > What exactly does WM mean by "represented by digits"?
> If all the digits of r are there, with their correct indices, then the number > r is there. Otherwise you have not defined the number by its digits but need > another definition, a finite one of course.
The thing is that one can have "all the digits there" everywhere outside of WMytheology but according to WM , not within WMytheology. Thus WMytheology and mathematics are disjoint.
> > Rationals do not all have a representation "by digits" in any one base
> Correct.
But there are still only countably many of them, so they can all be named, even in WMytheology.
But the set of reals is immensly larger than the set of names so most reals cannot be individually named. 



