```Date: Jan 24, 2013 8:29 AM
Author: mueckenh@rz.fh-augsburg.de
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)>> 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.  Int_j(j) the first j is identical with the second j. And both belong toa FIS of lines and columns, respectively. This holds for every j.Regards, WM
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