Date: Jan 24, 2013 8:29 AM
Subject: Re: ZFC and God
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)
> 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
As long as the line has a finite enumeration, also the column has. In
t_j(j) the first j is identical with the second j. And both belong to
a FIS of lines and columns, respectively. This holds for every j.