Date: Jan 24, 2013 4:22 PM
Subject: Re: ZFC and God
WM <firstname.lastname@example.org> wrote:
> On 24 Jan., 13:56, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> > "Jesse F. Hughes" <je...@phiwumbda.org> writes:
> > > Yes, but let's be perfectly clear here. What we have now is this:
> > > a function t: N -> R such that, for all i in N, t(i) is a real
> > > number with terminating decimal representation. We'll write this as
> > > t_i and we'll write t_i(j) for the j'th digit of t_i (in its
> > > terminating representation, which is, of course, unique).
> > > Let d in R be defined by
> > > d(j) = 7 if t_j(j) != 7
> > > d(j) = 6 if t_j(j) = 6.
> > ^ Should be 7, of course.
> > > Clearly, for all j, d(j) != t_j(j) and hence d != t_j for any j in
> > > N.
> > > Is this what you mean up 'til now?
> > So, for instance, take the obvious enumeration of finite decimal
> > representations (in [0,1), of course)
> > 0.0
> > 0.1
> > 0.2
> > 0.3
> > 0.4
> > 0.5
> > 0.6
> > 0.7
> > 0.8
> > 0.9
> > 0.11
> > 0.12
> > ...
> > Clearly, t_i(i) = 0 for every i, and hence d_i = 7 for every i. Thus,
> > d = 0.777..., which is a number without any finite decimal
> > representation.
> As long as the line has a finite enumeration, also the column has.
Nonsense. As usual from WM.